Welcome to the forum, sorry it had to be when your guy isn't doing too well =(
As far as his head, to me it looks as if he had scraped his head and is missing his scales there. Keep an eye on it to make sure it doesn't get bigger or red with sores.
As far as his gill.. never seen something like that. It could be just a simple cyst, or lymph.. but hard to say at this point. Again, would just keep an eye on it to see if it grows. If he starts showing other symptoms such as lethargy, not eating, losing color, etc then we could use those symptoms to help diagnose easier.
If you don't mind, a couple recommendations on your care. =)
For a filtered tank that size, you don't want to be doing 100% water changes, as then you can kill the good bacteria and end up doing more harm to your little guy then good. For a 2.5g filtered, 1 30-50% water change per week is enough. Dose with conditioner the full amount. Once a month siphon using a small siphon, or stir the substrate and use a cup to dip out the waste. Make sure to dose the water with a full dose (for that size tank) regardless of the % of water you are changing out.
When feeding freeze dried foods, it's good to only feed them once or twice a week, with soaking them in a tiny bit of tank water prior to feeding since they have potential to bloat their stomachs very easily. Same with flakes, you don't need to presoak, but feed a tiny bit since they can bloat them. Make sure you are using betta flakes, as tropical flakes for other fish don't have the proper nutrients/ingredients the bettas need.
If you decide to use AQ salt, it's recommended to put them in a smaller QT container with 1-3 tsp per gallon, with 100% daily water changes, no longer then 10-14 days, as using AQ salt excessively, or unneeded can harm the bettas internally such as with their kidneys, etc. It's unwise to use on a regular basis, and to not do the proper water changes when using it.
With winter approaching, you will want a heater. Bettas are tropical fish and require 78-82*F to thrive in. Anything less will cause lethargy and eating less as their metabolism isn't working fully. Also with winter, temps flux a bit more, especially when night comes.. and bettas don't do well with fluxes in temp. A small heater such as marineland mini heater
will work good for you.
Just wanted to throw those out to help you out a little more. I'm sorry I can't say for sure what is going on with his gills though. So using this to bump your post up and hopefully someone who may know will see it. Good luck!