This would definitely be faster, the i5 is a newer model, also this is a quad core processor compared to the dual core in the Mac mini. The ssd in this will also be faster than a standard hard drive.

It's pretty likely, yes. The last mac mini was released in 2014 but you're saying 2.5GHz so it's likely the 2012 model with an i5-3210m or 2011 with an i5-2520m. All really old chips, all dual cores.

The i5-6400t in this is a quad core so anything multithreaded will see a good boost but you should also see boosts on single-threaded tasks since a few generations of small improvements add up to a large improvement.

Using cinebench 11.5, single-threaded performance is better by a little less than 10% but multithreaded is better by ~70%

Yes, it would be.

Though the i5 6400T is sixth gen - this model appears to have been superseded by an i5 7400T HP Pavilion Wave model - and we are now just starting on eighth gen with much fanfare and excitement about more cores/threads, the dual core 2014 Mac Mini hasn't been updated since, well, 2014 (edit - I think your Mini is the 2012 model, rather than the disappointing 2014 refresh but the desktop i5 6400T CPU is more powerful than the 2012 Mini's and the integrated graphics are better, too, though you wouldn't want to play recent games titles with it). The Mini looks gorgeous and all that but, hardware wise, it is starting to look a bit anaemic. It's a pity Apple haven't updated it but that's music to HP's ears, no pun intended; the HP, or at least the model I saw reviewed, has a fairly decent integrated speaker, bass wise, and, with two integrated noise cancelling microphones, could be fun to use with Cortana as an alternate to Amazon and Google's assistants.

I have seen unflattering comments about that HP being a squished Mac Pro with a sweater made from office chair or car seat material but one advantage of the mac Pro design is the fairly large circular circumference allowed them to use a fairly large fan and keep it quiet. The shape of the HP means a smaller fan. In the I7 model, both CPU and included graphics card use the same heatsink and it cane get noisy. I would think the T-series CPU and its integrated graphics would make for a quiet experience. To get the best out of the integrated graphics, you would need to upgrade to dual channel memory (the HP uses a single 8GB stick of RAM, rather than 2 x 4GB dual channel.

I would be tempted to wait and see what - if anything - Apple do with the 8th gen CPUs with more cores/threads. I wonder if they would change the design, adding a speaker as HP has, to turn the Mini into a voice assistant like Alexa and Google. I imagine it won't come cheap, though. I haven't had hands on experience with the HP but it looks like an okay buy, if the design appeals to you. It's certainly original, to the point that I think most of the reviews that accuse it of ripping off Apple's trashcan design are being disingenuous. I would prefer the i5 7400T model, if it's available, but if it is available, I doubt it is selling for £400.

I haven't needed a burner for a very long time but you can get an external one for under £20 on amazon if you need one