I have a mongoose malus. It has a 36t chainring in the front and a 7 speed in the back. If I wanted to have higher gears can I replace the front chainring?
This answer is based on wanting faster gearing, higher ratios.
To go faster you need to have smaller/lower tooth count cogs on the rear cassette, or a larger chainring. Or both.
There is a physical limit of about 13 teeth for a freewheel and 11 teeth for a cassette. There are BMX bikes and folding bikes that can go as low as 9 and rarely 8 teeth, but they require special wheel hubs. SO if you're already on an 11 tooth small cof on your cassette, the only option is to upsize the front chainring.
Your main problem is clearance for a larger chainring. Firstly it has to clear the right-side chainstay. If that doesn't fit then you're out of luck. Start with a cardboard template to see how much lager a chainring you could fit.
Then check clearance in all other directions - your breakover clearance (how close you are to the ground) will decrease. Your front wheel will probably clear things, because it has to clear the pedal when in the forward position. Upwards should be fine, but depending on your frame check all possible.
If your existing chainring is rivetted onto the crank spider then you're stuck, and will have to buy a new crankset.
Otherwise you'll need to find the BCD of your existing chainring. Take it off and print this PDF at 100% then compare. You will get an answer like 64, 88, 94, 96, 102, 104, 120. If it doesn't match, check your printout was 100% scale.
Then buy the biggest chainring that will fit, that has the same BCD as your existing crank-spider.
Finally you'll need to add more links to your chain, so just buy one or two new ones.
Based on searches, its a 1x7 gearing. Twist shifters imply its a bit BSO, as do comments about early rust. Upshot - don't spend a lot of money on this bike.
This answer is based on "higher gear" meaning higher cadence, which means lower gear ratios and therefore easier to climb.
First, grab the rear derailleur and see how far away from the cassette's biggest cog it can go. Then estimate the maximum number of teeth that would be. If you over-estimate then the derailleur will hang up on it and that's bad.
note - I can't even find if this bike has a cassette or a freewheel. At 7 speed its probably a cassette, but I worked on a 7 speed Freewheel today so they exist.
You could try buying a smaller chainring, but that will loose you your higher gears for going fast. If you never use them, that's probably OK.
Another option is to replace the whole right crank arm and spider with a double or triple chainring. This depends on the interface between the bottom braket and the crank. Very likely its a square taper. Then you can either shift the chain by hand when stopped or you can try and fit a front deraulleur somehow. A band-on one should work, but you'll need to fab a cable stop and get a left-hand shifter and cabling too. I've done this on one bike and it worked perfectly. On another bike it was a total failure cos the frame didn't allow the FD to mount anywhere useful.
The other option is to work on your motor and get stronger, so the existing low gear is good enough. Remember going up hills is always hard work. You're lugging 40 pounds (18 kilograms) of bike up any grade - that's also more hard work.