The law in Cyprus favours the tenant over the landlord.
The estate agent or your lawyer will have a contract they prefer to use, but some landlords have their own. Before you make the final decision to rent, you should have sight of the rental contract. What if you're an occasional smoker, the subject has not arisen during your search for accommodation, and the contract you are about to sign specifies "no smokers"?????
Before you sign any rental contract, make sure you read it thoroughly - it should show the name and address of the landlord, the name and address of the tenant, the address of the rental property together with details such as garden, specific parking space, furniture and furnishings. The amount of rent and damages deposit, frequency & method of paying and the duration of the lease should be indicated. There should also be one section detailing the landlord's responsibilities and another one detailing the tenant's responsibilities. And of course, the final section is the "what if we can't agree" clause.
Some rental contracts will have penalties indicated - for instance, if the rent is due on 15th monthly, then if it's late, the landlord may charge x% until it's paid.
As you have expressed concern over possible eviction attempts prior to next year's holiday season, I am guessing that your proposed rental accommodation is fully furnished and equipped, because otherwise weekly holiday rentals just don't work - holidaymakers don't generally travel with their own bed, bedding, pots and pans stuffed into their suitcases!
If you are so bothered about the possible future actions of your landlord, why not look elsewhere and find a landlord you feel you can trust?
and we eventually ended up with 2 dogs rather than just the one.