It used to be (in VB6 version) that a ship with a jump engine could only jump ships up to the rating of the engine OR the size of the ship, whichever was lower (ie: a 8kt ship with a 15kt jump drive could jump a max of 8kt ships).
This limitation has been drooped in C#. A ship with a jump drive can now jump any ship up to the jump drive limit.
If the jumpdrive is military (as I assume in an escort) you can also only jump ships with military engines. If you have a tanker with commercial engines for example it would need its own jumpdrive or jumpship.
I want to stress the fact that the Maintenance Type of the ship does not matter, it is all down to the engine types. I've made that mistake in the past when not paying attention
Jump shock:
Any Jump will give the ships jump shock. During jump shock a ship has its active sensor, fire controls and jump engines disabled.
The Duration of jump shock is the following:
A ship making a standard transit will suffer a delay equal to: (120 seconds + Random 1 to 60 seconds) * Ship Bonus.
A ship making a squadron transit will suffer a delay equal to: (20 seconds + Random 1 to 10 seconds) * Ship Bonus.
See
here for the full rule posting.
In a combat scenario you want a squadron transit as this lowers the time spent in jump shock, and this is were squadron size comes into play.
For regular travel standard transit is fine.
Also for standard transit if you are using a jump tender to jump a no jump-capable ship the tender can be on any side of the point and the other ship can still make use of it.