You're quite right! An interesting contrast between the Italian 'passato prossimo' and the English 'present perfect': these are formed in similar ways (have had/ho avuto) but are often used to refer to different types of events or experiences. For example 'yesterday' would never be used with 'have gone'. Often the system allows you to practice things you've already learned in later skills...but what section did you find this in?
gone is always used in the present when used with has... eg he has gone to fetch her coat. She has gone to the hairdresser. Where has the cake gone!
Went is used as the past tense eg she went to see her father yesterday. He went abroad last week. He always went to market on Friday.
Changing has to had makes it past tense eg he had gone to fetch her coat. She had gone to the hairdresser. Where had the cake gone. Does this help?
Yes, indeed there is a past tense in Italian, you'll get there soon enough. Keep in mind, however, that often the tenses in Italian are not used in the same way. On Immersion, the Italian present needs to be translated with the English past. Just take it a step at a time. Best of luck.
Is andare an unusual case where the "I" version is matched to gender or does that generally occur in the past tense (andato, andata) of a verb. For example, present tense "io bevo" is the same whether the speaker is male or female. Does it become "ho bevuto troppo" and "ho bevuta troppo" in the past tense?
No, the ending in the past tense only changes for the verbs that use the auxiliary 'to be' rather than 'to have'. So since andare uses essere, the ending changes for gender and plurality, as does diventare (sono diventato/a, or siamo diventati) and many others. But bere uses avere, so it will always be ho bevuto, regardless of gender or plurality.