Bitte lass das Glas auf dem Tisch stehen.

Because this is the informal singular imperative of lassen, used when speaking to one person you address as du.

• Infinitive: lassen = to let / to leave
• Imperative with du: lass!
• Full sentence: Bitte lass das Glas auf dem Tisch stehen.

Other forms would be:

• Lasst das Glas auf dem Tisch stehen. = speaking to more than one person (ihr)
• Lassen Sie das Glas auf dem Tisch stehen. = formal singular or plural (Sie)

So lass is simply the correct command form here.

Because lassen is followed by another verb in the infinitive, and in German that infinitive usually goes to the end of the clause.

Here the structure is:

• lass = main verb in imperative position
• das Glas = object
• auf dem Tisch = location
• stehen = infinitive at the end

So the pattern is:

• lass + object + location + infinitive

This is very common in German:

• Lass mich schlafen. = Let me sleep.
• Lass die Tür offen stehen. = Leave the door standing open.
• Lass das Buch hier liegen. = Leave the book lying here.

Here stehen lassen means to leave something where it is, in an upright position.

So Bitte lass das Glas auf dem Tisch stehen means something like:

• Please leave the glass on the table.
• Please don’t take the glass away from the table.

The verb stehen literally means to stand, but for objects like a glass, bottle, or cup, German often uses stehen when the object is upright on a surface.

So the sentence does not mean make the glass stand up. It means let it remain standing there.

Because this sentence describes a location, not a movement toward a destination.

German two-way prepositions like auf take:

• dative for location: where?
• accusative for direction/movement: where to?

Here, the glass is already on the table, and you are being told to leave it there, so German uses the dative:

• auf dem Tisch = on the table (location)

Compare:

• Stell das Glas auf den Tisch. = Put the glass onto the table.
  
  • movement to the table → accusative
• Lass das Glas auf dem Tisch stehen. = Leave the glass on the table.
  
  • location on the table → dative

This is a very common difference between English and German.

In German, objects are often described by their position:

• stehen = stand upright
• liegen = lie flat
• sitzen = sit, for some objects/animals/people depending on context

A glass on a table is normally upright, so German says it steht.

Examples:

• Das Glas steht auf dem Tisch. = The glass is on the table.
• Der Teller liegt auf dem Tisch. = The plate is on the table.
• Die Flasche steht in der Küche. = The bottle is in the kitchen.

English usually just says is, but German often prefers the more specific position verb.

Das Glas is in the accusative case because it is the direct object of lass.

You are telling someone to leave what?

• leave the glass

Since das Glas is a neuter noun, its nominative and accusative forms look the same:

• nominative: das Glas
• accusative: das Glas

So the form does not change, but grammatically it is functioning as an accusative object in this sentence.

Yes, bitte is perfectly natural here. Its placement is flexible.

These all work:

• Bitte lass das Glas auf dem Tisch stehen.
• Lass bitte das Glas auf dem Tisch stehen.
• Lass das Glas bitte auf dem Tisch stehen.

The version with Bitte at the beginning sounds very natural for a polite request.

So the difference is mostly about emphasis and rhythm, not grammar.

It is grammatically an imperative, so it is a command form, but bitte makes it sound like a polite request.

Without bitte:

• Lass das Glas auf dem Tisch stehen.
  This can sound more direct.

With bitte:

• Bitte lass das Glas auf dem Tisch stehen.
  This sounds friendlier and more polite.

German often uses the imperative for polite everyday requests, especially with bitte and the right tone of voice.

No, that would not mean the same thing.

• stellen means to put/place something upright somewhere
• stehen lassen means to leave something where it is

So:

• Stell das Glas auf den Tisch. = Put the glass on the table.
• Lass das Glas auf dem Tisch stehen. = Leave the glass on the table.

Also note the case difference again:

• auf den Tisch = movement onto the table
• auf dem Tisch = location on the table

So stellen would describe putting the glass there, not leaving it there.

Yes. Besides the literal meaning here, stehen lassen can also be used more figuratively.

Some common meanings are:

• leave something where it is
  
  • Lass die Kiste hier stehen.
• leave something unfinished / not consume it completely
  
  • Er hat seinen Kaffee stehen lassen. = He left his coffee unfinished.
• abandon / leave behind, depending on context

But in your sentence, the meaning is clearly the literal one:

• leave the glass on the table

So this is a good example of how German often uses a very concrete verb combination that English may translate more generally.