Is there a way or an option for a non household sims to propose? I know your playable sims can ask they partner for a marriage, but can the partner ask your sims? While I was still playing TS2 there were couple of times when my sims was proposed, but that hasn't happen in TS3 yet. I'm kinda old fashioned and still like the guy to propose, without having them to move in first. In Generation you can ask your partners parents for they hand, again, this has not happen to me yet, does the non household sims ever ask or do I need to have move them in first.

Short answer is no. Everything to do with changing the relationship from romantic interest onwards (girlfriend/boyfriend, fiancée/fiancé, spouse) is blocked for inactives and non-autonomous. Since the Generations EP they can divorce on their own, but that's it.
bluegenjutsu at simsasylum.com made this mod that sets these interactions to autonomous. Maybe this will do what you want.
(You have to be a member of simsasylum to see the contents of the link I posted.)

Don't forget that with University Life, inactive Sims can break up a relationship on their own by a kiss.

Oh yes, I totally forgot that there are 50 ways to leave your lover but not that many to get one.

But wait. Inactives do go steady, propose, and get married, at least to each other. I've never seen them ever propose a relationship change to an active. Except at prom night, when the offer to go steady is always triggered. I also do use SP, so maybe that's what drives it, but does that really mean that in a vanilla game, no inactives ever pair up?

I've never seen an uncontrollable sim ask one of my sims to marry him/her, or even go steady or engaged. Once in a rare while, on one or two occasions (ever, since this game came out) I've had another uncontrolled sim ask the sim I was playing to move in with them. The first time was very early in the game, maybe Base game, and it was a friend of my sim. The last time it happened, which was just within the past year (last Fall, I think), it was on their first date! Cheeky fellow.

I had my sim accept.

When story mode is turned off, nothing like that ever happens. I've been playing without any story progression whatsoever for almost two years now and have never seen this. In fact inactives won't even reach the Romantic Interest state on their own, unless there are Sims around with certain traits like Inappropriate who can autonomously kiss Sims with whom they are not romantically involved already.
When inactives pair up it is story progression which does this.

Frankly, you shouldn't entrust sim autonomy with the power to begin relationships or propose, unless you think great timing is popping the question right after they've pissed themselves and the dog is currently licking it up.

Because you KNOW it would happen in that kind of situation.

Which matters to those who -- like a lot of us -- start their first household in the shotgun shack at 58 Water Lily in SV. As luck would have it, VJ Alvi has that trait and lives right across the street which has led to some real WTF moments for, er, someone I know.

Bummer. I have the story mode always on yet my townies never seem to get married or have kids. Which is why I have never really played the Daycare career lol. Most of the time my towns are full of old people and have to add families with kids myself.