1) I would suggest you go with HDPE/Poly pipes because they can last longer, not very cost effective to use stainless steel unless you are renovating your house. Also make sure your plumber provide Sirim approved HDPE/poly pipe to avoid issues in the near future. Because in malaysia, even pipes have lousy quality ones. Probably google first and check the pipes to be familiar with it before engaging a plumber to come and check. Would not recommend PVC as its a bit difficult when it comes to external piping, you can use PVC inside the house for shower and sink, i think should be ok, but to kitchen better use HDPE.
2) From water filter (if you have) use 3/4 pipes is sufficient enough, no need go above it. And 1/2 when connecting to sink and shower taps. 3/4 all the way from water filter to water tank, then branch out to kitchen, reduce to 1/2 for kitchen sink, 3/4 also branch out to toilets and then reduced to 1/2.
3) You can DIY if you know the layout and knowhow of pipes. If not easiest is to engage a plumber to come and do for you. Try to get a few options and prices to compare. Of course from word of mouth is better. Material wise i think wouldnt exceed RM500 actually. Unless you plan to change your taps and shower valves also. xD But either way, your whole costing wont be more than 1k if u DIY. If plumber come i estimate around RM2k for re-piping. See how difficult or how easy it is.