Yes — in Fak Huai, as anywhere in Thailand, foreigners can own condominium units outright (freehold), subject to the 49% foreign-quota cap on the total saleable area of each building. Foreigners cannot directly own land, so houses, townhouses, and land are typically held through a long-term (30-year, renewable) leasehold or a Thai company structure. Your agent can walk you through the right path for each listing.