Hi halfmoon01!
First of all, it's still fairly early days, so please try not to let any rejections get you down or stress you out too much at this stage, there is time to put out plenty more applications and secure a role if you keep focused. Not all the schemes will be ending soon; some won't even be open yet! Don't use that as an excuse not to keep applying, because it's really important you keep going with it, but it's worth keeping in mind if you're worrying about it.
In terms of how many jobs you should apply for, there's not really a set number you should be aiming for, as unhelpful as that may initially sounds. What you need to be doing is applying to as many as you reasonably can, but focusing on quality of each application over the quantity of them. I totally agree with
@alleycat393 that you should try to limit to one a day or every couple of days and make sure you're really tailoring them each time. Naturally if you're comfortable applying to more than that at a time then do so, but make sure you're taking breaks, and that you don't burn yourself out.
When I found myself struggling for time around university work on a particular day, sometimes I used to just spend 10 - 20 mins searching for job listings and bookmarking them to apply for in future; that can be a nice way to give yourself a bit of a break from applications, but also feel like you're being productive. It's also easier to fit into your day than a full application would be. If you're concerned about the quality of your applications at all, I'd strongly recommend visiting your university's career services and seeing if they're able to review an application for you, and suggest any improvements you might need.
For my journey personally, I put out most of my applications from September through December, and started hearing back from aptitude/reasoning tests during that time and onward to January, I was quite fortunate to have secured a job by January, but a lot of people I've spoken to secured theirs quite a bit later than that, so it's not a fixed process in the slightest. From a numerical reasoning perspective, I'm quite a mathsy person myself and studied a course that included some, so I didn't choose to prepare for them personally, but there are a huge number of resources out there that you can use to practise the aptitude tests;
this is one example, though I haven't tested it out!
Best of luck with it all, and let me know if you have any questions.
Shadow