tire car replacement pressure checker tool and refill and sun shade recommendations

wife and I have mitsubishi mirage 2025 hatchback

original tire got it of puncture destroyed in some shrapnel on the road?

how much would a replacement cost original? and is it safe to use the old one which was patched by the vulcanization center

also saw them use a pressure checker tool like a iron rod..said it should be 30 for all tires but they told me wife it's not necessary to weekly check the pressure and refill

I felt the car handles the road lighter sort of raised when all the tires were full isn't that better for fuel efficiency?

also is it worth it to have that tool at home and also one for refill automatically

lastly what kind of portable sun shade would you recommend to cover the car instead of the car cover

do you'll buy from shopee

newbie driver enthusiast clueless about regular maintenance please share your recommendations

can't do any 3rd part work I think because car is on monthly installments for 5 years