If the training content is about the basic knowledge training of the company's system and post, the company can't charge you for the training, and the company is obliged to provide these trainings to new employees.
But if your training is paid by the company to let you go outside for training, the company can agree on the training fee and service period with you. If you don't perform as agreed, the company can charge your training fee, which should not be greater than the company's training fee, but should be converted according to your service years in the company, so it must be reasonable for the company to charge this fee.
If the second company has signed a non-competition agreement with you, it must start to calculate after you leave the company and pay the non-competition allowance of 20 15 to 20 16 for two years. This allowance can be paid in one lump sum or monthly. If the company does not pay this fee, you can not fulfill your non-competition obligation. If the company pays this fee, you must fulfill this obligation, that is, you can't go to work in the work unit related to this industry.
It should also be noted that the company has signed a confidentiality agreement or a non-competition agreement with you. If it is a confidentiality agreement, you can leave it alone.
The company can't restrict you from resigning. If you want to resign, you need to apply to the company three days in advance during the probation period, preferably in writing, and you can leave evidence. If it's three days, even if the company won't let you go, you can leave directly. This is the right given to workers by the Labor Contract Law.
I hope I can help you.