Depends on your definition of heirloom. There are varieties which have been in existence for 150+ years. Potatoes however are normally grown by vegetative propagation. Most varieties are therefor hybrids which do not come true from seeds. Seeds are formed in the small tomato like fruit that follow the blooms.
No GMO on the market, but yes it can be done. There is some research in Europe on potatoes grown for starch.

Here is a link that might be useful: GMO research

There are many heirloom potatoes. By "seed", I assume you mean tubers meant for planting? I have linked one of the better sources below. Keep in mind, though, that potatoes are one of the main crops in Idaho, so there are restrictions on what may be brought into the state.

Here is a link that might be useful: Potato Garden

This site has ladies and gentlemen in its base who do their own hybridizing of plants, including potatoes.

Give it a read.

http://alanbishop.proboards.com/

Yes and you can get true seed potatoes. They are healthier plants when you from seed. I bought mine from http://newworldcrops.com/wp/shop/2012-tomatoes/#new

Does the seeds obtained from berries of True Potato Seeds produce tubers that are true-to-type?

I want to buy a particular variety of TPS and multiply the seeds so that I can grow a lot more of my acreage for the same variety. Does it work like that?

Yes, I just planted 4 varieties that I purchased from Seed Savers Exchange. To me they are the most reliable of any heirloom seed company in the world. You receive seed potatoes and then make sure you have at least 2-3 eyes per hole. Save some of the bigger tubers at harvest time and plant them next year. Will always grow true to type.