I am a foreigner and have bought some properties.
Over the last few years the rules and regulations for foreigners have become relaxed in Malaysia. Now it's very simple. Foreigners can buy any property they want in Malaysia subject to State Authority consent(subject to a certain minimum price dependent on the relevent state authority), which takes about 1-3 months depending where the property is.
So once you've put down your 10% on your property, you make this application to the State Authority, and there is a 99.9% chance it would get approved - it's just a formality.
That's it. That's the only difference between a foreigner and local buying.
Answering your second question about ownership coming with Visa. No, a visa and ownerhsip are independent. To make life confusing the Malaysia My 2nd Home (MM2H) program write-up by the government states that if you are approved for the program you have the right to buy two or so houses each bought for over a certain amount. It is a fact that you have the right to buy two properties anyway. You don't need to be on the MM2H to buy any properties.