You can say ごきげんいかがですか？”Gokigenikaga desuka?” or ごきげんよう ”Gokigen you” Which may be less formal. As for the other question, I don't really see a problem with that. It depends on whether you think it's been a long time, I say it to my friends when I don't talk with them for about a week or 2 and nobody complained so....

＊For "How are you?", I would use お元気[げんき]ですか?(formal) /元気?(casual)/お元気?(feminine) or maybe 調子[ちょうし]はどう？ ＊Probably you could say like 最近[さいきん]どう?/最近調子[ちょうし]はどう?/最近どうしてたの?/元気にしてた? for "How have you been?" (All these examples are casual) ＊is it ok to say "O hisashiburi desu ne" if you haven't talked to them for around 3 weeks (when you've previously had regular conversations with them) ＞＞Positive. ＊For "Long time no see", I would say お久[ひさ]しぶりですね。(formal)/お久しぶり。(normal)/久しぶり。(casual)/おひさ~。(slang?)/久々[ひさびさ]ですね。(a bit literary? and polite)/久々だね。(normal, a bit masculine)/久々。(normal)/ご無沙汰[ぶさた]しております。(formal)/ご無沙汰してます。(polite)/ご無沙汰ですね。(normal)/ご無沙汰。(casual)/しばらくですね。(polite)/しばらくだったね or やあ、しばらく。(casual)

It depends on context and formality, but yes, there are any different ways.