Fixing a Nissan sentra 2005 1.8s that was rear ended

My car was reared by a van that was being driven by a driver on a learner's permit.

The bumper and trunk covers are smashed.

I got in touch with their insurance and their inspector came by and quoted $1700 for damages payable to me for
my car(I was not at fault).

I have to get my car fixed for sure and am not sure how much it's really gonna cost me.

I have been reading about my model - nissan sentra 2005 1.8s - on online forums since the accident and have
some questions:

1. Does'nt my model have the issue of the head gasket blowing after ~50k miles?

If my model has this issue, how can I take a few precautionary measures to ensure this does not happen (or
happens much later?)

I cannot afford to buy an engine, even used, for $2k+, and if a few hundred dollars in fixes can delay the problem
from surfacing, I need to know what I can do

What further concerns me is I read an expert saying on a forum that "Some customers don't even know they have
a blown one till they come in."

Is there a way I could find out if my engine's head gasket is blown?

2. My engine makes a screeching noise for like the first 5 minutes after a cold start

It sounds exactly like many chalks writing against a blackboard!

3. My engine misfires reliably, atleast once, every morning when I do this the previous night: turn it on (cold start)
for a few minutes (~2-3 mins) to take it off the road parking and park it in our apartment parking instead.

I thought petrol engines did not have the same startup issues as diesel engines, so what's this about?

4. The battery dies predictably every 1.5 - 2 years.

The death is always sudden: one day after 1.5 - 2 years of purchase the car will not start up and will need to be
jumped. The only solution is changing the battery.

This has happened only twice so far (I have had the car for 6 years)

5. In my last inspection 4 months ago, the inspection report said my "rear suspension (or it could be shock
absorber) is ripped". I have no idea what that means but it's a $500 fix!

I have discussed all of these issues with the nissan dealerships in my area and while they have denied #1, they
quoted me $700+ for fixing #2, #3 and said #4 could only be due to misuse of the battery.

I do not misuse my car: I don't run the radio/AC when the engine's not running and use my car to drive to and
from school everyday. No accidents so far. I don't drive my car hard as I WANT it to last a few more years and just
can't afford another.

Please also recommend any issues I should be careful about and any other fixes/inspections that I could get
done to keep my car in good condition.