Clarify "zum" vs "zu"
I understand that zum is zu + dem (dative)
But how about in this sutuation
"Ich suche einen Platz zum essen" - why zum and not zu?
It's "Ich suche einen Platz zum Essen". Here Essen is the noun das Essen.
If it was "Ich suche einen Platz zu essen". It would mean that you are trying to find a place and eat it (the place).
E will be capital when you use Essen as Essen is used as das Essen in this case . As zu is dative article it takez zum Essen . But it is also correct but not used to say Ich suche einen Platz zu essen .
Poleon21 is right in that it's "das Essen" here, but it's not "das Essen" = "the food", it's a nominalised version of the verb "essen". Not "a place for food", but "a place for eating".
You can just as well say, "einen Platz zum Ausruhen / zum Fischen / zum Parken" ("a place to rest / for fishing / to park in").
"Ich suche einen Platz zu essen" is grammatically wrong, it neither can be used to say "a place where I can eat", nor to say "a place that I can eat". Except if it's bible-style outdated speech as in "Suchet das Reich Gottes zu erlangen" ("Endeavour to attain the kingdom of God"), so: "I endeavour to eat a place".
(The last bit is part of an old joke. The teacher asks the students where the kingdom of God is. A student suggests it's in the town of Erlangen. Teacher asks why, student says that it's written, "Suchet das Reich Gottes zu e/Erlangen." In which "zu Erlangen" is an outdated way to say "in Erlangen".)