Is it possible to have relationship without children

Yes it is possible.

Yes

Sort of.
Really depends on how you define "relationship" and "children."

Sometimes when people ask about "relationships" what they're asking is "is it possible to just remain in the early infatuation stage where we're constantly excited, love being around each other, overlooking flaws, constantly turned on and having sex, and just take pleasure in each other?"

And when talking about "children" some people only mean human biological offspring.
Not considering "fur babies," or career(s)/hobbies as replacement "children," although they ultimately should.
Take people that found their partner on OLD or in forums like these, but stick around OLD sites, or on forums. Sometimes that's a form of "cheating," and continued attempts to fulfill what the relationship is missing because they "settled." For others it becomes their "baby," what they have to spend more time supporting, building psuedo bonds and relationships with. It is a separate relationship, but related to the relationship.

So if you're asking "is it possible to have a deeply connected, pair bonded, romantic relationship that lasts our entire lives where there are no offspring, and there are no instances of infidelity, arguments, break ups and getting back together, it's healthy without a lot of delusion and rationalizing, and it's a perpetually fulfilling, happy, blissful, and content, relationship," then no.

If you're asking "can I find a relationship with an expiration date, it's all good, and there's no children involved," then yes.

If you're asking "can I find a deeply connected, pair bonded, etc. etc. relationship where over time they don't have a wandering eye towards something to provide more fulfillment as they get acclimated to and build a tolerance for the relationship, seeking out other means of emotional, social, and mental validation, or purpose to the relationship outside of their partner?"
Then no.

Yes

Of course it is. If you need children to hold a relationship (or marriage) together, the serious issues are not the children.

Why not? There's your answer