"I like reading by the sea."
Translation:Én szeretek a tengernél olvasni.
If you say "A tengernél olvasni szeretem" you would need an object in the sentence. Szeretem ezt a könyvet a tengernél olvasni.
A tengernél olvasni szeretek. This is more correct, but still a bit strange word order. I think it means something like: When I'm at the see, I like reading. (and not running, for example).
Szeretek olvasni a tengernél. This would be fine :)
And to answer your question more directly, infinitives are not treated like definite nouns.
"Szeretem olvasni a .... -t" - "I like to read the .... "
You do need an actual noun(-like word).
If it is the reading itself that you like, you make a real noun of the verb:
"Szeretem az olvasást" - "I like reading"
Which you can also say with the infinitive, but then with the indefinite conjugation:
"Szeretek olvasni" - "I like to read"
Yes, all correct, you got it!
Although I would reorder you first sentence as:
"Szeretek kék könyveket olvasni".
It feels more natural when the object comes before the infinitive. I think this is generally true, but it needs to be tested.
Your second sentence works both ways, it is more of an emphasis thing.
So the definiteness, even though it applies to the olvasni, gets marked on the finite verb because that's the only one that can get so marked. Similarly to how Szeretlek nézni where the -lek gets marked on the finite verb even though it "really" (semantically) belongs on the nézni.
If I follow what you mean (not sure), I think that is correct.
Yeah, the "szeretlek nézni" is a special case. I think there is even some debate among linguists whether it ("-lak"/"-lek") belongs to the definite or the indefinite conjugation. But let's settle with definite. A good test of what the normal solution would be is to switch to another object (target person), other than the second person:
"Szeretem nézni őt."
Or even just the formal you:
"Szeretem nézni önt."
Basically, we have a situation where two verb+object constructions are nested in one another: to watch something and to like something. The "inside" structure changes to infinitive.
Btw. "Szeretem olvasni." is also a valid sentence, but it is an incomplete one. The implied object had been mentioned before.
Igen. Szeretem olvasni (a könyvet).