Juan, Since you have a hard disk (not an SSD or a hybrid) in your Mac, I would consider getting another hard disk, simply because you can get a 1.0 TB disk pretty cheap and it will have more capacity than your current one. As you see in the guides, it's actually pretty simple to replace the hard disk: (1) open the case (2) unscrew two screws to release the hard disk (3) carefully remove disk and then detach cable (4) transfer four screws from disk to new disk (5) re-attach cable, re-fit hard disk into its space (6) replace bracket (7) close case Done. From another computer, you can also download the OS Install from the App Store and then copy it to a USB (8 GB or more). Then you can plug it, turn on the Mac, and install. I've done this hundred's of times, it takes about 10 minutes to replace the disk, 30 minutes to install the OS. Good luck!
Battery estimates vary widely depending on what you are actually doing. 10 hours is probably not "normal use" but some utopian fantasy. If you want to make your battery last longer, turn of unnecessary services like Bluetooth, wireless, close applications which update regularly (like Mail) and close any applications or web browser tabs that you're not actively using. Batteries also degrade over time, so it also matters how old is your device?
Try looking in > About this Mac > System Report and look for the "WiFi" section. If you see something like "no hardware found" that means that your wireless card has become detached from your motherboard. You can open up the laptop and make sure the cable is plugged in. If you see information about your wireless card, then you may have some software which is blocking or turning off your wireless card. You'll have to google that or provide us with more information.
Are you using Windows 10? If so, this seems to be a very big bug that's been floating around since late 2015. I'm trying to find a solution, too. If you press Control-Alt-Delete, do you get a blue screen with options like "Lock", "Sign out", and "Task Manager?" If so, can you start Task Manager? Maybe you can see some programs running there that shouldn't be.
There is a difference between "crashing" and "turning off due to loss of power." I would not describe this as "crashing." It's not *too* surprising that your computer is switching off at 10%, because it's trying to preserve your log in session before it *really* has no more battery. Also, I've found that battery estimates can vary a lot. Just learn to plug it in at 20% so that it never reaches that threshold. Also, look for "coconutbattery" and see some important information about your battery. It may be exhausted.