Israel: How safe are Tel Aviv and Jeresulem between Christmas and New Year's?

I have lived in Israel for over a decade and do not recall this period of time as ever being associated with any specific rise in activity. In other words, whatever safety advice/precautions you would treasure at any other time apply equally. And I would consider things to be as safe (or dangerous, depending on how you want to frame things, who you are, where you want to go, and what you want to do, etc) as the week before or the week after.

It is difficult to answer, and we lack some information which are probably also illegal to ask (e.g. about your ethnicity and religion: these matter for this topic) [and please do not add such information].

In general it is safe on touristic places (check touristic guides), especially if you look like a tourist (this is contrary of most safety rules around the world: the conflicts are mostly with local people, and both want to keep tourist friendly: both need money from tourists).

Get daily information from hotel staff about demonstrations and clashes, and avoid such zones.

It should be safe. If you want to cross the wall, thing could change, but also on other small villages on Israeli side. Still safe on most touristic places, but I would avoid going alone: some people could react badly to every foreign, or you could just do involuntarily something offensive/disregardful (e.g. of local customs).