Is it normal to be paranoid about this?

No not really a normal thing to worry about with no extra context.

Push comes to shove it's not really your business where she goes in the short term.

I know, but she didn't give me any other numbers that could be called in case anything goes wrong in the house, so it adds to my paranoia.

Yeah she doesn't need to give you multiple numbers, you already have 1. You're living in their home, not babysitting their kid or planning a trip together.

Am I right in thinking you don't actually have any reason to presently contact them?

I don’t really follow why it’s necessary to catastrophise just because someone left the house for a couple of days.

Because I am the only other person in the house and haven't been given enough information on how to handle those sort of things.

If it’s an emergency with you, you call the relevant emergency services.

If it’s something wrong with the utilities you turn them off at the mains, (fusebox, gas feed or stopcock), and then decide whether you need to call a relevant tradesperson.

I don't know where it is...I am simply very scared

Because I don't know the head landlord. If there is a pipe burst or short circuit, or an accident happening to me in the house, who is going to come and address it immediately?

None of these things would really be the other tenents responsibility tbh.

You asked if this sort of paranoia is normal and it's basically not, you seem to be MASSIVELY over thinking this stuff. Like when Admit-One talks about fuse boxes and taps and you say you don't know where they are... the simple solution is to go and look for yourself. You can't really expect the other person to be instantly reachable 24/7

Not sure if it's simply paranoia or separation anxiety.

How do you have separation anxiety from someone you purportedly met a month ago?

Also as a tenant you should be aware of who to contact if you need to report a maintenance issue etc. That's your responsibility - you can't just palm it off onto another tenant. You should know who the letting agent/property manager/landlord is for reporting those things, and as noted otherwise for genuine emergencies you would contact the emergency services in the first instance, not them.

You need to be responsible for your own life, it is not your flatmates' responsibility to take care of everything.

Also as noted this is a really disproportionate response to a very minor and every day occurrence. You may want to discuss with your GP why you responded in this manner rather than a more measured way.

I have every reason to get worried because I am the only other person in the house.