Once you receive DOS recommendation letter, you can start H1 application.
You can apply for 140 long before J waiver. J waiver is only the prerequisite for 485 stage.
2) 我想回國一趟去,但擔心簽證出現問題,請問我該在J1 waiver後回好,還是在H1換下來回比較好?十分感謝。
If your J does not have enough time, may encounter some trouble. Always safe after H1 approval.
3) 對了,補充一點,10年前,我曾申請F1簽證,結果在北京被鋸數次,最後的理由定性為移民傾向。請十分感謝!問這經曆對我下次簽證影響大不大?
If you use H1b visa, no worry at all.