Partial answer:
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Do Ukrainian Г and Belarusian Г have the same pronunciation?
In general — no.
Belarusian Г is usually considered to be voiced velar fricative [ɣ].
Exact nature of Ukrainian Г is debated. Some claim it is voiced glottal fricative [ɦ], while others — voiced pharyngeal fricative [ʕ] (both sample sounds in Wikipedia represent Ukrainian Г badly). Also pronunciation of Ukrainian Г may vary, depending on word etymology and speaker's dialect, sometimes it may turn into Belarusian-like [ɣ]. But most agree that in the "canonical" dialects of Ukrainian language in majority of words (excluding cases of borrowed words when it's sometimes pronounced as [ɣ] just because of mimicking pronunciation of original language, e.g. Greek) it differs from Belarusian Г.
(However in mid-schools Ukrainian children are usually taught that Ukrainian Г is a voiced counterpart of the Х [x]. Not because it really is (it is not; Belarusian Г [ɣ] is), but rather because no other Ukrainian consonant fits this role better — and such a simplified view is enough for mid-schools.)
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Do Ukrainian Ґ [Belarusian Ґ] and Russian Г have the same pronunciation?
In general — yes. It is voiced velar stop [ɡ].
More info: Ukrainian phonology.
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There is "alternative sound of Г" in some words of the Russian language (ага, угу, бог, господь). What type of Г is it?
The "Russian phonology" Wikipedia article says it's either [ɡ] (strict), or [ɣ] (like Belarusian).
While the "Ge (Cyrillic)" Wikipedia article says it's region-dependent: /ɡ/ generally, /ɣ/ in the Southern Russian dialect and may be /ɦ/ in the regions bordering Belarus and Ukraine.