You could try to get an extension while there but it is unlikely to be granted as it is not extendable (though in India you never know). Best to use an agent.

You may be able to leave the country (e.g. fly to KTM) and request a new e-visa (2 are allowed in one year). But there also is a rule that requires a break between trips so not sure if this will work either.

Do not overstay. If it was a one day overstay immigration at the airport might give you some leeway - but 15+ days will cause significant issues (hefty fines most likely).