die Platte
plate / slab
A flat, usually rigid piece made of a material such as wood, metal, stone, or plastic.
Die Granitplatte für die neue Küche wird morgen geliefert.
The granite slab for the new kitchen will be delivered tomorrow.

plate / record
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plate / slab
A flat, usually rigid piece made of a material such as wood, metal, stone, or plastic.
Die Granitplatte für die neue Küche wird morgen geliefert.
The granite slab for the new kitchen will be delivered tomorrow.

The many meanings of 'Platte' (plate/slab) are all based on the basic idea of something flat and broad. Knowing this helps you understand unfamiliar compounds like 'Herdplatte' (hotplate) or 'Druckplatte' (printing plate).
Stell den Topf bitte auf die heiße Herdplatte.
Please put the pot on the hot hotplate.
In many colloquial meanings, 'die Platte' is an abbreviation for a longer word. The context makes clear whether a 'Schallplatte' (record; music), a 'Festplatte' (hard drive; computer), or a 'Plattenbau' (prefab apartment block) is meant.
Meine alte Platte von den Beatles klingt immer noch super.
My old Beatles record still sounds great.
In the context of music, typical verbs are 'eine Platte auflegen' (to put on a record), 'Platten hören' (to listen to records), or 'Platten sammeln' (to collect records). It often refers to a vinyl record as opposed to digital formats.
Ein DJ legt den ganzen Abend nur alte Platten auf.
A DJ put on only old records all evening.
When 'Platte' (platter) is used in connection with food, it refers to a large serving platter. The type of food is often named in the word, as in 'Käseplatte' (cheese platter), 'Wurstplatte' (sausage/cold cuts platter), or 'Fischplatte' (fish platter).
Zum Empfang gab es eine große Käseplatte mit Früchten.
At the reception, there was a large cheese platter with fruit.
The term 'Platte' for a bald head is purely colloquial and is often felt to be somewhat casual or joking. Typical phrases are 'eine Platte bekommen' (to start going bald) or 'eine Platte haben' (to have a bald head).
Er macht sich Sorgen, weil er langsam eine Platte bekommt.
He's worried because he's slowly starting to go bald.
The colloquial term 'die Platte' for a residential building made of prefabricated concrete slabs is especially common in eastern Germany. The typical phrase is 'in der Platte wohnen' (to live in a prefab block).
Meine Großeltern haben 30 Jahre lang in der Platte gewohnt.
My grandparents lived in a prefab block for 30 years.
In geology and the natural sciences, 'Platte' (plate) refers to a tectonic plate of the Earth's crust. The combination 'tektonische Platte' (tectonic plate) is almost always used to avoid misunderstandings.
Japan liegt an der Grenze mehrerer tektonischer Platten.
Japan lies on the boundary of several tectonic plates.
album
'das Album' and 'die Platte' can both have to do with music. An 'Album' means the collection of songs as a musical unit, whether you listen to it digitally, buy it on CD, or own it on vinyl. A 'Platte', by contrast, is the physical vinyl sound carrier. The words can be confused because an album can also be released on a record. If you are talking about the songs or the release, 'Album' fits. If you mean the vinyl object, 'Platte' fits.

Wir haben auf dem Flohmarkt eine alte Platte von meinem Lieblingssänger gefunden.
We found an old record by my favorite singer at the flea market.
Das neue Album der Band läuft bei mir seit gestern fast den ganzen Tag.
I have been playing the band's new album almost all day since yesterday.