DDog is also a JRT cross, and he was initially a 'borrowed' dog, and eventually became mine permanently. I have to say that everything seemed a lot more stressful when he was borrowed, and I had someone else to answer to rather than being able to use my own best justment! Nowadays he's occasionally lent to DF, who doesn't listen to a word I say, so DDog comes back fat and disobedient
That's not to say you can't train someone else's dog - you definitely can when you're talking about a few days a week - it's just that it helps if you can have some consistency between the two households (e.g. in terms of words used)
Should I always keep him away from other dogs as I am not his owner/very experienced
What does the owner do when they walk the dog? Is he off lead and with other dogs? If so, I'd be aiming to do the same, once you're confident the dog will come back when called. If possible, it would be great to go out walking with the owner and do some recall training (e.g. a game of 'ping pong' where the dog runs between the two of you on command, and gets a treat each time).
DDog had no recall whatsoever when I first met him, but laissez-faire then-owner pretty much gave me carte blanche to do anything sensible with him. After about 6 weeks of on lead walks (by which time we'd definitely bonded), I cracked it in a day - a walk with lots of recall practice on an extending lead, before taking him to a semi-enclosed area, letting him off and doing some off lead practice. He must have eaten his own bodyweight in treats that day
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Dog interactions tend to be much more relaxed when off lead, for two reasons
a) the flight vs fight response - dogs on leads know they don't have the flight option, so will more readily resort to fighting (the flight may be no more than a couple of metres, but it's important!)
b) being on lead restricts the full range of body language that dogs will use to communicate, leading to misunderstandings
It would be useful for you to watch some YouTube videos on canine body language - there's just so much that we don't pick up on if we don't know what we're looking for!
With regards to squirrels and birds, I have to say I regard them as fair game for chasing. DDog has never caught one, and I have to say that dogs don't tend to bark at prey when they're running at full speed after it...