>Could I get someone to fix the windows and then send the bill to my landlord?

Yes, but it isn't quite as easy as that. You give written notice, there's a time frame, then you have it done, you pay for it, then you take it out of rent. Talk to a tenant group to find out exactly how it's done. /u/pullmantenantsunion is one that I know of.

Here's our state's Tenant Landlord Act