since you live in Turkey and the risks / consequences of getting outed are probably severe, I would encourage you to consider having a designated safe person / friend who can clean & keep the clothes for you, ideally a female friend or a male friend with sisters who can swing that? Are there any LGBT+ groups or centers that you know about where you could maybe connect with people who could help you with these logistics?

I wouldn't use certain anti-microbial, moisturizing hand soaps for cleaning clothes, but yes - a simple bar soap is probably fine for washing clothes (I have used simple bar soaps to hand-wash my clothes without issue, you just have to be prepared to scrub and rinse them many times to get all the soap out, which incidentally also gets the dirt, sweat, etc. out.)

Don't underestimate the risk of your parents going through your things when you're not there, even for reasons you wouldn't expect. (For example, my parents went through my backpacks and possessions without my knowledge or consent, and then tried to justify it by saying they thought I was abusing drugs, even though I never had used drugs and there was no actual justification or reasoning they could provide for why they thought that, let alone accountability on their end. They also took my private journal - so be careful about what information you write down or leave around - including your lemmy account, etc.)

I've hand-washed clothes in the sink before. I just used regular bar soap, a basin of warm soapy water and gentle working on the parts of the clothes that tend to get sweaty + any visible soil. The more you let the soap do the work, rather than your hands, the better the clothes will hold up. Repeat the wash if the clothes are too dirty, my metric is if the water is too gross for me to bathe in after washing, wash again. Usually not necessary unless the clothes are really gross. Rinse in clean water. Wring out as much water as you can to reduce the drying time, just be careful not to stretch them too much. You can hang them over the back of a chair to dry, for smaller things I used the supports of the chair legs too. directing a fan at them makes them dry faster. It doesn't have to be a powerful fan, just enough to keep some air moving over the fabric. I found it helpful to drape the clothes over the back of the chair and let one side dry, then flip it over to dry the parts that were in contact with the chair. Make sure they're completely dry to the touch before you put them away so they don't mildew. I'll second the recommendation of putting them away ASAP and don't leave them lying around when you're not there. Parents are snoops and they usually suspect more than they let on. If you have ziploc bags or watertight containers you can also stash them outside the house, if you have a place that you can access securely. Going for walks through the woods helped me find places and gave me plausible reasons to visit them regularly.

P.S. I forgot to add, it may be a good idea to wipe the chair off before you put the wet clothes on them if you live in a dusty area. I may have unwittingly walked around with some dust stripes a few times 🙃