I am under impression, that unlike in historical middle ages, the land estates in Westeros are neither splitted among several children, nor combined. Basically, the heir inherits all and if another title comes their way, it goes to a hetherto landless sibling. Am I right?
More or less. Holdings are seldom divided. Nor are they combined, as a rule, although one person could concievably hold more than one title. The other major factor is the current lord -- if one decided to do something unusual with his estates, that would carry weight. (Might also cause disputes, though)
Yet being a landless son of a noble family doesn't prevent one from marriage (as it did in the middle ages). So, is a lord in Westeros bound by law and custom to support his relatives with a designated portion of his income?
No. Some do (the Freys, the Lannisters). Some don't (Gregor Clegane with Sandor). Some put their excess relatives to work (the Freys again) in the castle, or give them vassal holdfasts (the Starks and Targaryens).
And if so, why aren't excessive relatives shunted into the Faith, Citadel, etc. in order to concerve the family fortune?
Some are. The Freys again. The Tyrells as well.
Also, what about dowries?
What about them?
And what's the difference between landed knights (Ser Gregor Clegane) and very small lords (i.e. Lord Baelish the Elder)?
The title. A lord has greater powers of rulership over his domain (the power of pits and gallows, it was called in some medieval cultures) Lord would generally be considered the more prestigious title. A knight is (or was) a fighting man, however; that title has its own specific martial and religious meanings -- and in a culture that reveres the warrior, its own prestige. Not all lords are knights.
A landed knight could concievably have greater holdings than a small lord.