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?
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 Except if it's bible-style outdated speech as in "Suchet das Reich Gottes zu erlangen" ("Endeavour to attain the kingdom of God"), so: "I endeavour to eat a place".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 In which "zu Erlangen" is an outdated way to say "in Erlangen".)