敷島の日本の国に人二人有りとし思はば何か歎かむ is always translated into modern Japanese as some variation of 大和の国にあなたが二人いると思えたら何かを嘆こう and I'm wondering why is 思はば translated as 思えたら. Why not 思ったら? -aば is the conditional form right? What's the difference?
You are correct that 思はば in classical Japanese is basically a plain conditional ("if I think"). However, in this context, it has a mood of counterfactual assumption ("if I were to think...", "if only I could think..."). The author was in despair because there was only one あなた in reality. The Japanese language does not have a direct equivalent of counterfactual subjunctive in English, and the simplest way to explicitly express this counterfactual mood in modern Japanese is 思えたら or 思えるなら. あなたが二人いると思ったら without のに would sound like the author actually started to believe there is another あなた ("now that I think there are two anata...").
This 何か歎かむ is a rhetorical question ("what will I grieve about?" → "I won't grieve about anything"), so its modern literal translation should be 何を嘆こう, not 何かを嘆こう.
EDIT: I think it's possible to use 思ったら in combination with のに to translate this waka into modern Japanese (あなたが二人いると思ったら何も嘆かない(でいい)のに), but then the rhetorical question part would have to be less literal.
思える is 可能動詞(potential verb). It means "can think".
The nai-form of godan inflectional paradigm verb + れる(auxiliary that means "potential") changes to potential verb.
For example, the nai-form of godan inflectional paradigm verb 読む is 読ま(ない). 読ま + れる`changes to a potential verb 読める, which means "can read".