You can find the extensions under the "Settings" tab: the right-most tab. The first three entries there give access to the extensions. When clicked, a screen with description of the extension opens up, with in the top-right a button with the price on it. Click that button to start the purchasing process.
Note that after purchasing the Airspaces extension, it can take a couple of minutes until they are downloaded and appear on the map; possibly longer with a slow internet connection.

The most likely cause that the extensions are blocked, is because you have disabled in-app purchases on your phone. You can enable them again in the Settings app, under General→Restrictions. You only need to enable them temporarily during the purchase.

Yes it does. First of all, it enables a more stable altitude display. The pressure information is synced with the GPS altitude before flight, to get a baseline. Then during flight, the altitude is only derived from the pressure sensor, as required by many competitions. See more details here.

The vario is also derived from the pressure information, but that was more difficult. The pressure sensor in the iPhone is extremely slow: it reports only one sample every 1.3 seconds, and it lags about 3 seconds behind the actually movement of the phone. As a consequence, I had to base the vario support in Flyskyhy mostly on the accelerometer data, using the pressure only as a reference. The result is a decent vario, although it cannot compare to the reliability of a Bluetooth vario.

So far, only an iPhone version is available. Porting the app to Android would be a major undertaking both in time and costs. This is both because of the differences in operating system between iOS and Android, and because of the larger variety in hardware models running Android. Therefore, I have no plans right now to release Flyskyhy on Android.

The app is developed for iPhone, and does not have iPad-native support yet. That means it will run on iPad, but in "iPhone compatibility" mode, just like any other iPhone app.

You can add waypoints manually, both on the waypoints map screen, and on the waypoints editing screen. But Flyskyhy also supports loading waypoint files in various formats. If the waypoints file is available on a web site, simply open the link in Safari on the iPhone, and it will ask whether you want to open the file in Flyskyhy.
If you have the waypoints file on your computer, you can e-mail it to yourself, and then open the attachment in the email app on the iPhone.
Or you can use iTunes to transfer the file to Flyskyhy. Drag the file to the screen in iTunes where the Flyskyhy flight log files are visible. Make sure Flyskyhy is already running when you do that. 

Before your flight, press the Start button. This indicates to the app your desire to start a flight, and will put the app into Flight Mode. The app will check a number of things, will fix the screen orientation into place, enable vario tones, and ensure continued operation in the background even if you switch off the screen or close the app. The log does not record the period before you take off. It starts when you move faster than 3 m/s (11 km/h, 6.7 mph) for more than approximately 10 seconds, and will include the 20 seconds before that as well.
During flight the Start/Stop button will show the flight duration in hours:minutes.

To stop recording a flight, press the Stop button. If you accidentally press the Stop button while you are still moving, you will get a warning. 
If you have enabled automatic flight end, then the log is automatically stopped after your landing.

In order for Flyskyhy to function normally, and flights to be logged, it needs to have access to location information. That sounds easy enough, but a number of settings in the Settings app need to be set correctly for that:

• Location Services needs to be enabled, both in general and specifically for Flyskyhy. They can be switched on under Privacy→Location Services.
  
• Background refresh must be enabled, both in general and for Flyskyhy. You can find that under General→Background App Refresh.
  
• Airplane Mode must be switched off, otherwise the GPS does not work either. You can switch Airplane Mode on/off on the control panel that appears when you swipe upwards from the bottom of the screen. 
  

Flyskyhy has a variety of different vario tones to choose from. But note that these are mostly intended to be used with external varios (see below). Vario tones are only useful if they help you find thermals. Traditional variometers achieve a high degree of accuracy by using a pressure sensor. The iPhone (before version 6) did not contain a pressure sensor, and therefore lift and sink information needs to be derived from the altitude obtained from the GPS. This information is not sensitive and responsive enough for the purpose of finding thermals. Therefore, although the vario tones work with only the GPS data as well, without an external vario with pressure sensor they will likely be only confusing, not helpful. 

Flyskyhy supports SensBox, FlyNet, GoFly iPico, XCTracer, BlueFlyVario, and SkyDrop bluetooth varios. You can select whether Flyskyhy or the bluetooth device should generate the vario tones (or both, if you like). Flyskyhy has a selection of different tones to choose from, besides the standard tone. You can also choose whether to use the GPS data from the vario (if supported), or from the iPhone. If you know of another vario which works with Apple devices, then let me know, and I will add support for it. See more details here. 

You do not have to buy them again, simply tap on 'Restore Extensions' under the Settings. Make sure you are logged in with the same Apple ID as you used to purchase the app.

It is very hard to say anything definitive about the battery life. Besides type of usage, iPhone model, and battery capacity, it depends on the outside temperature, and the quality and age of the batteries. But here are some indications from my own experience (no guarantees can be drawn from this information):

• with no external battery, an iPhone 4S will last about 2 hours.
  
• with a 2350mAh external battery, an iPhone 4S will last about 4 hours (I have a clip-on battery with velcro on the back side; very handy)
  
• with a 8800mAh external battery, the iPhone 4S will last at least 7 hours
  

All these are with both the internal iPhone battery and the external battery fully loaded at start, and with the screen on all the time.

You can transfer flight logs to your computer through iTunes.
1) connect your phone with your computer and start iTunes
2) select the phone icon in the top left
3) select the Apps menu entry on the left
4) scroll down, and you will see Flyskyhy in the list of Apps under File Sharing. Select it.
5a) now you can drag any .igc file from the list on the right to a folder window.
5b) you can also drag any .igc file from your computer into the list, and it will automatically be added to the logbook in Flyskyhy.

Of course, you can also email individual files to yourself directly from the app to transfer them.

The landing and launch sites in Flyskyhy come from paraglidingearth.com. If you add the site there, then Flyskyhy will eventually pick it up. Because this is partly a manual process, it can take up to a couple of weeks before it is visible in the app. If you want to speed up the process, then let me know on the support page after you have added the sites.

This is likely due to a side-effect of the hands-free function. The hands-free function makes it really easy to switch pages during flight: simply hold your (gloved) hand shortly over the top of the phone. However, there are a number of restrictions due to the way Apple has built this. If you hold your hand there too long, then the screen goes black, and it does not work at all in landscape mode. Also, when you use a phone holder that covers the top of the phone, then that will also trigger the function, and the screen keeps changing or goes black. You can switch the function on/off in Settings→Other→Touch-free control. 

Please let me know what feature you would like on the support page, and I will consider adding it.