Breakdown of Dudo que haya mucho respeto en ese grupo.
mucho
a lot
en
in / on / by (means of transport) / about (after pensar)
que
that (relative pronoun, conjunction)
el grupo
the group / the band
Questions & Answers about Dudo que haya mucho respeto en ese grupo.
Why do we use haya instead of hay here?
The phrase Dudo que (I doubt that) expresses uncertainty, which is a classic trigger for the subjunctive mood. Because you are doubting the existence of respect, the normal present tense hay (there is) changes to its irregular present subjunctive form, haya.
I thought haber meant "to have". Why does haya translate to "there is"?
You are right that haber is normally used as a helping verb to mean "to have" (like in "I have eaten"). However, it also has a special impersonal form that means "there is" or "there are". In the indicative mood, this word is hay. In the present subjunctive, it becomes the fully irregular word haya.
Why is it ese grupo and not eso grupo?
Grupo is a masculine noun, so it takes the masculine adjective ese (that). Eso is the neuter form of "that", which is only used for abstract ideas, unknown objects, or general situations. You never put eso directly in front of a noun.