Yes, you can get high-speed internet. Most internet cafe's have broadband/DSL. For home use, there are several companies offering 3G, which isn't super-fast but it's pretty much adequate. If you're around KL, I'd recommend going with IZZI - they actually have 4G, which is faster than the 3G, and they don't require a contract. Whatever you end up with, avoid Celcom - service is unreliable and customer service is non-existent! You could also pick a plan with TM, but I think that all of their plans require that you have a land-line, which I never had, as well as a 1 or 2 year contract.

You can get cable TV through Astro (Astro :: Making Your Life Richer) - all sorts of English channels.

As far as local banking goes, you have to either be in Malaysia on a MM2H visa or an employment visa, or you can't bank locally. I stayed in Malaysia for 2 years on a social visit pass, so no one would let me have a bank account in the country (though I've heard rumours that Standard Chartered allows foreigners to have Malaysian accounts with them without a residency visa). What I ended up doing was opening a Singapore bank account, which I could do without any special visa (DBS was happy to do this). But you can also get by quite well by using your regular bank and just accessing cash through ATM's. If you think that you'll be wanting a local bank, be sure to bring a letter of reference from your bank back home - it will make it easier when you apply for a foreign account.

Hope this helps!