For your first question, it will be legal for the company to fire you under the grounds of retrenchment. Retrenchment is the act of cutting down losses by an employer to save his company, more commonly known as downsizing. However, it has to be proven with sufficient ground under the Labor Code before such retrenchment can be considered valid, like severe economic losses and other financial reasons.
As you have said in your story, your low productivity is directly connected to the number of students your company assigns to you. Since January is a time of low enrollment as you have said, the company may use such as grounds for downsizing to avoid serious economic losses. Basically, retrenchment ang gusto nilang mangyari.
Secondly, kung papalabasin nila na nagresign kang voluntary, mawawala yung separation pay benefits mo under the Labor Code. That is their end game, para di na nila babayarin yung separation pay mo since it is required in retrenchment to be paid.
If you can, please go to the nearest regional DOLE office if you need more clarification regarding your labor issue and para magkaroon ka rin ng possible representation under them if they see that you have a valid labor case that should be filed.
Good luck on your situation.