Learn English – What’s the difference between “be up to” and “get up to”

Consider this exchange:

Speaker 1: Thank you.  
Speaker 2: That's all right!

In this case, speaker 2 is very casually acknowledging that speaker 1 has thanked them. It is somewhat lighthearted. This is similar to, but less polite, than an actual "welcome":

Speaker 1: Thank you.
Speaker 2: Welcome!

These are both very informal and and would not be used in a professional or business setting, or where you do not know the speaker well. It is considered much more polite to say "you're welcome" when you are thanked.

In the second case:

Speaker 1: Thank you.
Speaker 2: All right.

I would not say this, it definitely comes across as rude. In this instance, it is only an acknowledgement that speaker 1 has spoken, without speaker 2 offering any sort of welcome in return. It would be the equivalent of:

Speaker 1: Thank you.
Speaker 2: Ok.

It's always better to be polite in formal situations. I always say "you're welcome" to everyone.

Anyone: Thank you! 
Me: You're welcome!

To answer the second half of your question:

When you agree someone's proposal, you would say "OK" or "All right." What is this sentence short for?

Answering someone's proposal with "OK" or "All right" generally means two things:

1) You have confirmed you understand what they are talking about.
2) You are agreeing with their proposal.

It is a colloquial shorthand for saying "I understand and I agree."

The usual basic pattern is tell someone. We can add another complement to the verb, if we want, and use tell someone something:

• Tell Bob.
• Tell Bob (that) we need to leave.

We don't usually use tell something without saying which person we were telling.

• *tell (that) we need to leave. (wrong)

The pattern is the other way round with say. The basic pattern is say something. If we really want to add a person, we can say say something to someone, or say to somebody something. Notice that we need to if we include the person we are saying it to.

• He says (that) we need to leave.
• He said (that) he was leaving to me.
• He said to me (that) he was leaving

But we can't say someone.

• He already said me. (wrong)

The original example sentences

What did he _____ ?

What are you _____ ?

In both of these examples, the questions are about the information that was given, not the people that were spoken to. For this reason we need to use the verb say:

• What did he say?
• What are you saying?

So, the patterns to remember are:

• tell people
• say things

Note: There are a small number of 'things' that we can tell. For example we can tell: stories, jokes, lies, the truth - and other words that mean similar things to these. Notice that if someone said He told us a joke, but we didn't hear the last word in the sentence we could say: What did he tell? There are also different senses of the verb tell. One of these for example is to 'detect' something. This has a different grammar.