Hi In Wroclaw,
that the landlord can enter if I fail to respond to an inspection request, and a few other ods and sods. Are these normal?
It can be normal, I have done this in the past.
2/ Landlord not present
They do not need to be present.
I would strongly advise that you get the power of attorney or the contract allowing this third party to represent the landlord otherwise he really could be anyone.
In case of emergency (accident, incident, inspection) and / or the inability to contact the tenant, the landlord has the right to enter the premises without his knowledge.
If you want to be more careful, you could ask to have the inspections in writing a month prior.
As for the 'emergency inspection', that could mean floods, fires, gas leaks etc... you could ask to clarify it in the contract.
4/ Each Party shall have the right of early termination of the contract for the previous month's written notice occurring at the end of the calendar month.
Will you be registered in the property?
I am not certain this is totally legal in Poland but it is standard in contracts.
5/ For late rent or other amounts due under the lease, later than by more than 35 days, the landlord may terminate the contract with immediate effect without notice.
Have them change that to written notification two weeks (or one month i.e. the deposit)) rather than effective immediate.
If I pay cash for the first rent and deposit when I get the keys, surely I can expect a receipt?
You have to, otherwise there is no proof you paid.
If the landlord is paying tax, you could ask for a Faktura.
How do I get the landlord to register me at the address with the required civic office?
You will need the landlords signature or the POA giving the right to a third party to sign on behalf of the landlord.
Registering in a property is not ideal for landlords, you get different rights, especially if you are a single female parent.
Obviously I do not know the full ins and outs of your contract but to get them to clarify and negotiate 'reasonable' timelines would be my over all advice.