Is it ethical/legal to use the University's resources for a personal project?
It's unethical to use your university's hardware resources and then not share with them the eventual proceeds of that research. If the work you do were to produce papers, then they would share in the reputational advantage for employing you and being affiliated with your work. If it would produce a patent or a product, then employment rules at my university in the US would have us split ownership and royalties. At the very least, the university bought the equipment, paid the power bill, and paid someone to administer it. Ethically they deserve to benefit, too.

Now, I have no idea what the laws of Israel or the regulations of your university have to say about this, so you should check before you do anything.

When it comes to software (the solvers in your question), things may be different. If the software is open source under a usual license, you may generally use it for any purpose you like. Open source licenses typically do not regulate use at all, and only cover redistribution. If the software is not open source, then, in the US at least, regulation of use is generally left to the copyright holder. Any permissions that you have to use that software flow through some sort of explicit (written down) or implicit license. If someone at your university gave you software owned by the university and told you to use it for your project, then generally speaking you may use it in the course of your employment as directed by your supervisor. You probably cannot use such software for a side project without permission from the copyright holder.

Your employment agreement, contract, or university regulations will govern whether or not personal projects somehow become property of the university, shared property, or are kept entirely separate due to your use of university resources. Most universities actually want their researchers to pursue interesting ideas, but if you use their property, they want a cut of the resulting profits or an ownership interest in any intellectual property. In the US, the Bayh-Dole Act guarantees that inventions made through federally funded research can be owned by the grantee rather than the US government, and most universities pursue this ownership. I don't know if Israel has an equivalent law.

The ethics here are pretty clear to me. Don't use other people's property to make a profit without sharing the profit with them. The laws and regulations are local, so ask your boss, administration, etc. about the local rules.