I've never seen a pump setup quite like that, and I've seen a lot of them. Either way, my recommendation is actually to install a submersible pump, here's why:
Assuming it's a jet pump sitting there (I'm not sure what else it would be) like the one above, it would be better to move it inside mainly for environmental conditions. The electrical connections are also not rated for outdoor/wet conditions, and frankly it looks unsafe because there's potential someone could touch water around it and be electrocuted.
There's actually two types of jet pumps: shallow well and deep well, and each has a different challenge in this case.
Shallow well jet pump
Shallow well pumps only have a single suction line, but can usually only lift about 5.5m (total vertical distance). Depending on how much higher the house is from the well, this may not be an option.
Deep well jet pumps
Deep well jet pumps can lift much more as the name implies, but have two lines going to the well. Unless you already have two water lines going to the house, or are willing to trench another one, this probably isn't a good option.
It looks to me like the best option would be to install a submersible pump.
You already have power at the well (which is typically the biggest challenge with converting from jet pump to submersible), it only requires a single water line, and submersible pumps are better in several ways: more powerful, more reliable, no noise in the house, and never have to be primed.
If you only have two wires (plus ground) going to the well, you'll have to use a 2-wire pump, which is slightly less reliable because it has the control circuitry in the pump. 3-wire pumps have a control box in the house (where it's simple to replace if needed) but as the name implies, require 3 wires (plus ground).
You'll also need to move the pressure switch, but that's fairly simple.
Cheap interim solution
If you want to perhaps put this off and get a bit more time, you could consider just moving the pressure switch inside, or just installing a new one inside and bypassing the pressure switch on the pump. It's not going to reduce wear on the pump or the conditions the motor is in, but hopefully it'll avoid a pressure switch failure.
Pressure switches cost tens of dollars and installing one requires only fairly basic plumbing and electrical skill (you can ask a separate question if you'd like more info on just how to do that).