Should I study Mechatronic Engineering?

Yes definitely go for it. What I have observed so far in engineering are the mechanical engineers who do not know electronics and electrical engineers who scare any mechanical formula or design. Mechatronics train you for both aspects. Go for it. Biomedical engineering is good too.

If I were starting over I would probably do mechatronics.

Yes, You should definitely do that as it will be beneficial to everyone involved.

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It sounds really interesting too. If you know you want to become an engineer, then definitely research this. Talk to people who work in the field if you can find any. Utilize every resource at your disposal and weigh the pros and cons before making a final decision.

Yes, if you like it.

I would recommend a BS in Mechanical Engineering and take the mechatronics courses(controls, systems, dynamics, instrumentation) as your electives. Mechatronics approach is the only way to go for modern machine design. I am afraid most employers won't understand what a Mechatronics degree means, and feel comfortable with a BS in Mechanical Engineering.

Many people decide on a field of study without a good idea of what it can involve. I suggest you start working on your own projects to gain some understanding about what engineering can involve.

There are many electronics kits available online that give you the materials and capabilities to make a robot. Some kits give you the base knowledge and others give you the specific materials and tutorials to build a robot and are often able to add on with more materials.

A simpler kit that can be programmed by the Arduino IDE or a version of BASIC is best with which to start. If you already know how to program in C then that is a possibility.

There are a number of sites that have tutorials on building robots and cover electronics.

Nah play video games, dark souls 3 is the bomb