Choosing a Buddhist partner ain't beneficial to spreading Dhamma?

So why Buddha speak about qualities instead advising people to find Buddhist partner that could one of the way to spread Dhamma?

I don't get the impression from the suttas that, at the time, the Buddha counted on lay-people to even really know what the Dhamma is, let alone to propagate it.

Very generally speaking the function of lay-people was, at best, to be virtuous and to support the monks (and so be able to hear the Dhamma, to take refuge, and so on).

Note that the suttas which we have are as were recorded by monks (at the "councils"), so...

One another question is if both partners are from different religions then how they could lead their children?

If you exclude violence, perhaps some of the fundamentals of ethics and wisdom may be quite similar across different religions -- see Golden Rule for example. Something like the sutta of the six directions may be good advice and well-said, but it seems to me universal, i.e. advice that might come from any parent of any religion.

Or, if or where ethics are not compatible across different religions, it was enough to say "look for a partner with compatible morals" (without specifying "compatible religions").

Also, to a certain extent, there were no "Buddhists" at the time when the Buddha was advising people.

I guess a main difference between different religions is in the different "rites and rituals", but I'm not sure that matters in the grand scheme of things (i.e. there are more important topics to be concerned with).

Another difference (between religions, or between Buddhism and other religions) is in the doctrine or view, of eternalism for example -- but maybe that (view of eternalism) isn't very far from what Buddhism might call "mundane right view", which I gather was maybe about the best you might expect from a lay-person anyway.

For practice if one finds a friend— prudent, well-behaved, and wise, mindful, joyful, live as one all troubles overcoming. --SNP1.3

It seems to me there is no simple answer for this one because there are many subtleties and possible scenarios. Some first thoughts...

It would all depend on what sort of religion people are practicing. A Christian and a Buddhist might be indistinguishable or utterly distinct depending on their approach to religion. A Buddhist believes there is only one true religion since there is only one true doctrine and its proponents may be called Christians, Buddhists, Sufis, Taoists, Muslims or have no name at all.

If we take the view that it's all about discovering truth then names don't matter. In real life, however, many religious folk are dogmatic rather than truth-seekers and where this is true it seems best to marry within our own belief-group to avoid endless arguments.

If a Buddhist and a Christian feel they cannot marry then I'd suggest that one or both of of them is misinterpreting the teachings of the founders. The Dalai Lama does not recommend that we abandon the religion of out birth for Buddhism or insist that we marry within Buddhism. Why would he? But marrying someone with similar spiritual or life goals and the same level of seriousness is bound to be sensible.

And in the end marrying another Buddhist is not going to help spread the Dharma unless we know enough abut it to know how to choose a partner. Buddhists are advised to spend their time with people of like-mind and helpful character but there's no mention of the name of their religion.

Good to see that Nyom Swapnil seems to do fine.

The way to really support and be able to transport the Dhamma is to leave house and walk the Holy Life.

Why should the Buddha give advices for different dangerous path one might like to choose?

And yes, to grow in Dhamma is not a matter of birth or religion/tradition one has grown up in, but a matter of past nissaya paccaya, even more 'strong condition cause' (upanissayapaccaya).

[This is a gift of Dhamma, not meant for trade or exchange]

Spreading/growing dharma to others is not an obligation of a Buddhist. Only place it needs to grow as far as you are conserned is in yourself. You gain very little if not nothing by others following it.

If you want others to see the light, best thing you can do is to become the light.