The answer to your question is No. Those sentences are not possible. 'Dare' is a semi modal. This means that it sometimes behaves like a regular verb followed by a 'to' infinitive ( as in 'Dare to dream') and it sometimes works as a modal ( as in 'How dare you?' or 'I daren't ask'). When it is used as a modal, it takes the bare infinitive. 'How dare you?' can stand alone or it can be followed by the bare infinitive. The sentences you've given are wrong. The correct version is 'How dare you TALK to me like that?'. This is the only possible form of 'talk' which can follow 'How dare you...'. If you come across an example where it sounds like there's a conjugated verb following 'dare', there is probably a break between the two: "How dare you? Talking to me like that! It's disgraceful." The first words, 'How dare you?', stand alone as an exclamation, expressing indignation. The next section 'Talking to me like that!' is a fragment which is grammatically unconnected to the exclamation.

I agree with Greg, but technically, the verb after "dare" should be the "bare infinitive"--the infinitive without "to", not the simple present. That's why we say "how dare he say that" instead of "how dare he says that".

Both sound very awkward to me. After "How dare", personally I always expect the simple present "How dare he say that!"

How dare you? This is called an interjection or exclamation (!). They can take different forms and use voice and mood, or lack sentence structure entirely. They're a kind of outlier in terms of grammar because they don't really follow any sort of rule. See here: https://www.thoughtco.com/interjections-in-english-1692798 "How dare you!" is a sentence - it uses the interogative mood (the form of a question) but it is incomplete. As a complete sentence it would have a complement phrase as in, 'How dare you speak to me that way!' But it is maent as an expression or exclamation of shock so it takes the ! marker instaed of the ?. The sentence is used as an exclamation to sate an objection to the way someone has spoken. The main verb is 'dare'. He dared to speak. S|V|C(vp:inf) The thing to notice about the verbs in this sentence is that dare is the main tensed verb and to speak is an untensed verb phrase. It definitiley indicates an action but it is an action as a thing (technically it is an object complement (S|V|OC). He dares to speak. He has dared to speak. He will dare to speak. See what I mean? So, the second untensed verb phrase is a verb complement - He dares "something", where the object takes the form of a verb phrase (infinitive form). Hope that helps.

"How dare you talk to me like that!" is the correct way to say it. I would say it's correct for both present and past. It doesn't sound right to me to have the verb in the past tense, even when the action occurred in the past.