Now this one is tricky

I'll do my best to point out some important points, but I still strongly suggest that you get a lawyer with a good command of family as well as international law. You are planning to get married, so I discuss this as if you already were. As long as you are not married, you are left without nothing in case of breakup or death. Only a common child would give you some rights, simply living together has no implications.
Rule number 1). By Finnish law, what is yours is yours and what is his is his. No matter what. Everything else is an exception.
Prenup. A prenup is meant to keep rule no. 1 in effect in case of death or divorce, which would otherwise result in separation of properties, then distribution of matrimonial assets and finally inheritance. A prenup is a very very good idea, but in your case you seem to want the contrary.
Distribution of matrimonial assets. This is the thing that some people call the 50/50 rule. Bit like that yes, but actually not that simple. You are not entitled to half of your husbands property, but entitled to have some of his property transferred to you until your net worth is equal to his, but that is the case only if your husband is richer than you are. If you are richer, then he is entitled to some of your property! Now I do not know if your property in Latvia is counted to your net worth, this is one matter where you need international law expert. I believe it is (thus bad for you considering the fate of the house). With a prenup, you waive your matrimonial right to his property and he waives his matrimonial right to your property. But what you want is to KEEP the matrimonial right to the house, so you need a prenup with a special clause or a completely different solution.
Important exception to DOMA rule. In case of death, the surviving spouse is never obliged to pay or give anything to heirs of the deceased, even if he/she is richer.
Inheritance. Children inherit it all, if there are any and there is no will. All that is left after distribution of matrimonial assets, that is. Keep concepts clear here, do not confuse DOMA with inheritance. Many people do, and lots and lots of unnecessery and erroneous forum post are written.
Legal share. 50% goes to children even if there is a will.
"Can't be kicked out of house"-rule. In case of death, the surviving spouse cannot be kicked out of house by anyone, if that house is a common home of the married couple. As he officially lives in Estonia, then is it officially your common home? Another point you need an expert for. This rule applies to right of use only, ownership transfers as normally.
Gift tax. You are paying off the debt of your bf without getting any property in return. That may be considered a gift, and gifts are subject to gift tax. It takes a very pissed off vero bureucrat to collect the tax in your case, this is merely a worst-case scenario. But you have been warned.
Recommended options:
1) Make a prenup. Not a regular one, because of aforementioned reasons. Do a special one that states that everything that you own is outside of matrimonial right except for the house. This way you get at least 50% of the house no matter what, and you get protection for your apartment in Latvia, that is if Finnish law is applied. If Latvian law is applied, then I don't know.
2) Do 1 plus ask your bf to make a will, giving the house to you. Now you get at least 75% of the house, and if you have enough money to pay the value of remaining 25% to your bf's son, he must accept the money and cannot demand a share of the actual house, so you get 100%.
3) Get some of the house transferred into your name, as a sale or as a gift. Take taxes into consideration here. It might be thought that you have been purchasing the house piece by piece by paying the bills. But ask an expert, as this is the most trickiest option of these three.
EDIT: Additionally, I'd recommend that you make a will of your own just in case you happen to die first. That way, your husband won't inherit your apartment but you can give it to anybody you like.
Prenups are registered at the magistrate.
He has a son, which means that if something happens to my boyfriend, again everything goes to his son and I am left without a place to live.
If you get married and live together, you are protected by the "Can't be kicked out of house"-rule. Provided that Finland is the country of your residence right after marriage, that is!
If something happens to both of us, then still those who are supposed to inharit something from me, are also left with nothing and everything again goes to my boyfriend's son.
Won't happen, this can be rationaled from the rules above.