As with most IE languages, English uses radically different forms of the verb to be in different tenses, moods, persons, and numbers. I’ll make a short list the various examples in English, and add what I assume to be the related forms in German or Danish. Note, I don’t give the particular tense or whatever because those are not the same between different langauges.
[ul]
[li]English am German ??[/li][li]English are Danish er[/li][li]English be, been German bin, bist[/li][li]English were German war, waren[/li][li]English was German gewesen [/li][li]English ??? German sein, sind, sei[/li][/ul]
Are there any English dialects that still use a cognate of German sind?
The OP’s not looking for translations (yours are correct, by the way) but for cognates, words which look alike and have the same meaning in two languages (as opposed to “false friends,” which look alike but have different meanings). The only example from the OP that I’d consider a cognate is were:waren. I’m not sure that be and sein have the same origins, though; any German etymologists out there?
WAG - some of the german verbs appear to be Latin derived - sind ~ sunt, so there may be an older/alternative German dialect which contains the cognates you’re looking for, rather than the reverse.
Another place to look might be nordic languages - the Swedish word for is sounds like are (no idea how to spell it).
Old English had two verbs for “to be”: wesan and béon. However, béon fell out of use, and is currently only used in the word “be”.
Wesan, in Old English, only had the present tense (beon was used in other tenses) It had the following forms:
(I) eom
(you) eart
(he, she, it) is
(they) sind
Later, in Middle English, wesan replaced béon, and was extended to the other tenses as “was” and “where”.
Wesan is the same root that the German words for “be” use: sein, war, gewesen (“is, was, been”). It is also used in the word verwesen (“to rot”).
So, “am”, “are”, “is”, “was” and “where” are forms of an old verb, wesan, which is also the root of the German words sein and sind. Not that you’d guess it just by looking at them.