Your sentences use the modal auxiliary verb can (or its negative form can't or cannot). The only form of a verb that can be used after a modal verb is the bare infinitive. Notice my use of be used after can in my previous sentence. Be is the bare infinitive of to be. And used is the so-called past participle of to use.
As for your first sentence, we also see the bare infinitive be after the modal verb can (in its negative form can't). And after be you find the so-called present participle having. Here having actually does refer to present time. This is because it draws its "tense" from the tense of the finite verb of the verb phrase it is in, and here that verb is the present tense can.
Can can express at least three things: possibility, ability, and permission. In your sentence, it most likely expresses possibility or ability, so paraphrases of your sentence include
It's not possible for me to have this conversation with you.
I don't have the ability to have this conversation with you.
Which of those two meanings is the actual one depends on the context in which it is stated. Note that your sentence can also express exasperation or frustration on the part of the speaker.
Your sentences 2 and 3 are ungrammatical because the count noun walk requires a determinative before it, such as the article a or the demonstrative pronoun this, which you've used in your other sentences. Sentence 4 is ungrammatical because after be you need to use a participle, such as having.
Sentence 3 (I can't be having a walk) is a possible example of can't expressing permission, or–with can't–the lack of permission:
I'm not allowed to have a walk.
Let's look at Sentence 6
I can have a drink with you.
First, notice the bare infinitive have after the modal can. The sentence can mean any of the following, depending on the context:
It's possible for me to have a drink with you.
I have the ability to have a drink with you.
I have permission to have a drink with you.