Let's assume that Jane successfully maintains her crown as Queen of England and Ireland.
What events are likely during her reign?
The big question is how long Northumberland can dominate her. She disliked her husband, his son Guildford. Northumberland had many enemies and would make more. Jane might reach out to them, and thus instead of going down with him as his puppet, help bring him down and even become leader of the anti-Northumberland group.
Then she has to get rid of Guildford. Possibly he is condemned with his father.
Northumberland has her chopped right away.
Do we see an earlier Armada?
No.
What happens with Elizabeth?
With Mary gone, she's the rightful heir. That makes her a threat. Northumberland may want to chop her too, but on what grounds? He may try to use her against Jane - do what I want or I'll replace you. It would be amusing to see them make common cause against him, but that's too good to be possible. One question is: how ambitious was Elizabeth in her own right? How much did she want to be Queen?
Because the situation is very dangerous for both Jane and her. If Elizabeth is recognized as rightful Queen and takes power, it means Jane is deposed as a usurper and gets chopped. Jane for her own safety may chop Elizabeth.
Wildcard scenario: Jane decides she really wants out from under Northumberland and Guildford, and conspires to elevate Elizabeth as part of the anti-Northumberland coup. The Dudleys get chopped, and Jane blows town, having formally recognized Elizabeth. Then again, Elizabeth or her faction may take no chances and chop Jane anyway. She's just too dangerous.
The one thing favoring co-existence is that they're both Protestants. Neither has to worry about the other rallying the other religious faction.