Yes, I think the matx motherboard would fit.
The full case is an attractive one. It looks to be fairly well ventilated.
Yes, there are some solutions for front panel connections.
But, and this is a big but. The power supply looks to be proprietary and will not work out of the box on your new motherboard. Possibly adapters are available.
Then, the psu will be minimal, and ok for a 1050ti that does not need aux 6 pin power.
It looks to me like you will also need a new psu.
Do not buy a cheap psu. Look for a unit with a 7 to 10 year warranty and you will have a long term investment.
Yes, it will be expensive.
Since you are on a budget, you really may not need a case initially,
Just put the parts out on a table.
A $5 switch can...