If you rely on a fast internet connection, you should use the o2 availability check before you decide for a new apartment. The o2 availability check shows you for each checked address which maximum speed is likely to be possible via which connection technology at the address. To do this, click on the small "i".

The monthly base price refers to a specific product according to the product information sheet and not to a specific speed. This means that even if the maximum product speed cannot be reached at the connection address selected by the customer, the same product price applies. 

I checked, and it says that I have access to the 50 mbit, which should be good enough and is what we were supposed to have. The question is mainly how can I switch from DSL to LTE since apparently the O2 employee gave me wrong or incomplete information.

May I see the screenshot? Make sure that it shows “über DSL”!

@blablup it says that I can get maximum 16mbit with DSL but 50mbit with Home Spot 4G. That’s the one I want to change to, the DSL is not important as I’m aware is not possible to get more than this in my region.

If you no longer wish to use the DSL contract, you can terminate it at the end of the contract period by observing the period of notice. Mobile radio communication services cannot be used with a DSL contract. 
In addition, you should bear in mind that mobile radio communication has some restrictions compared to a DSL connection: No minimum bandwidth, all mobile radio communication users in a cell share the available bandwidth, no public IPv4 address, no IPv6 and much more. 

@blablup Our contract just got renewed for another year so terminating it doesn’t seem to be an option. It says this in the O2 website though:

So I imagine we should be able to change the technology without changing our contract and free of charge, no?

Your imagination exceeds what o2 offers. A technology change from DSL to mobile at the customer's request is not offered by o2. 

@blablup it’s not my imagination, it’s literally what’s written in the image I just sent from their own website.

In the case of o2 my Home LTE contracts, o2 is entitled to switch the contract to DSL supply without the customer's consent. This option is intended for the case that the customer consumes too much mobile data volume and thus restricts the use of the mobile phone cell by other customers. 
This changeover is made at the request of o2, not at the request of the customer. 

However, such a case does not exist in your situation. You already have an o2 DSL connection that meets the contractual conditions. 

@blablup I see… is it possible to somehow terminate my DSL contract then, maybe paying a fee, considering it was renewed last month to start a LTE contract?

Such an arrangement would have been most appropriate in the context of the move. But you can still contact the o2 customer service department about this now. 
However, I would definitely advise against concluding an o2 my Home LTE contract with a minimum contract term, as it is unclear whether such a makeshift solution will meet your expectations. I would rather assume that this is not the case. 

@blablup Thanks a lot for your help! :)