I took those 4 plus an additional class (Poli Sci. maybe) in one semester, and I did fine. It will be a lot of work, but it's not "suicide". As a senior in engineering, trust me, it will get MUCH worse as far as difficulty and workload go. It's really just good practice for your time management skills for upper level coursework, where you will take 5 upper level engineering classes in one semester.
As far as taking classes at other schools, make sure and check with your counselor about which classes from which schools are applicable to count in place of the TAMU classes. Most engineering departments at TAMU are really strict about transfer credit involving physics/science/engineering.