There are may ways to filter tap water, but as you may have learned from my posts, I am all about simplicity. If I lived in an apartment, I would probably use the Pall .2 micron filter that fits on the tap, as a lot of members do. You can read the discussion here:
https://connect.mayoclinic.org/discussion/recommendation-for-0-2-micron-filters/
For away from home, I use bottled spring water, but have been looking at the Lifestraw bottles to cut down on plastic waste.

I don't use a steam bag for my parts, I use a saucepan on the stove. You can search "bololo" or steam sterilizers to learn what other members have to say.

I wash reusable water bottles with a brush (to disrupt any microfilm trying to form) then sanitize in my dishwasher on the sanitize cycle which includes heated drying. My dishwasher temp is 145F. If away from home I sanitize with a bleach soak. The bottle brushes go into the dishwasher too. I learned this many years ago from friends who hike in Arizona, where they have to be careful about desert fever, which is as nasty as MAC to get rid of.