Hi hisprincess and welcome to the forum
I'll try an answer and hope others more experienced in areas you are concerned with will also post.
1. It is OK to shower but not really recommended to drink...everyone uses Aqua from bottles. I brush my teeth in tap but probably, until conditioned, you're best to also have a bottle in the bathroom. Cooking with boiled water is OK but again probably best to use the bottle. Nearly all villas use large 19 litre bottle chiller/heater dispensers.
2. There are many internet providers in Bali, mostly in the habitated area in the south, but it gets a bit spotty further out. There's also 3G and I believe in some areas 4G. I use CBN fiber to my villa in Kerobokan and it's OK.
3. Avoid Kuta/Legian then...you might like laid-back Sanur as it hosts a mix of senior and more mature visitors but still has a nice beach and entertainment/restaurants etc.
4. Cannot answer...not knowing your expectations. Food, clothing and transport is fairly cheap. Accommodation can be anything from a rooming house to a villa. After arrival you can see what's available from grocery stores or western frequented pub/restaurant adverts on walls. Any realtor will have a portfolio but they need commission so probably not the best deal. It's a buyer/renter market as a lot available.
5. I've used Bali_Mode for all my visas....(owner..Didik Supriadi)
www.balimode-biz.com ....email
balimode@hotmail.com. He has offices in Kuta, Ubud and Jakarta.
The Sosbud is renewable but requires going to S'pore, or some place outside RI, and return. If over 55 an annual retirement Kitas is available.