Every place is different, so depending upon where you enroll in your online classes you'll find different answers to your questions. I'll try to answer them based upon my experience. When I was in community college for my first two years of undergrad, I took several psychology/sociology/philosophy courses online so that I could earn my AA simultaneously with my AS.
1.) As for reputable places, look for universities and colleges that offer the courses online, not necessarily "online colleges." I'd look at your local community college or state university and see what they offer online.
2.) I never took a lab course online so I'm not sure about this. My girlfriend took a human biology course online through the community college and she just had "labs" that she had to complete at home. She also took a chemistry class where she and a group were required to meet once a week wherever was convenient and complete a lab. The school provided all the equipment and materials at the beginning of the term, and besides submitting worksheets and a formal report they were required to submit a photograph of all the group members and the products of the lab. Another community college I know offers lab sciences online and you have to actually go to the college once a week for a lab/recitation.
3.) Sometimes tests have to be taken at a common location during certain times and are proctored. For pre-requisite classes, some vet schools require that this is the case. For my humanities/social sciences classes that I took online, all the exams were online as well. Some of the professors were very explicit in saying that you were allowed to use the book and any other available resources on the exams. Others might not have said that or might have outright said that you couldn't, and in those cases the questions were more comprehension and critical thinking than straight out of the book questions, so using the book wouldn't be much help anyways. In every case the exams were timed, and would automatically submit what you had if you didn't finish on time.
4.) Grading was the same as all my other classes. Homework, papers, tests, etc. were assigned a point value and you got scored on them and graded just as you would a land-based course.
5.) The instructors could get creative with homework. For example, in one of my psychology classes there was a software program you had to buy that had modules you had to complete and then answer questions about. There were always, always papers, sometimes several for one class. The module format was pretty common, and in each module you were given assigned readings, questions to answer, and activities to complete in order to receive credit. Then the modules ended in an exam and there was a final at the end of the term. Oh, and a lot of times there were discussion forums where you had to make a certain number of posts per module. For example, in one class you had to start your own topic and reply to someone else's each module.
6.) All of mine were self-directed learning through reading the chapters and keeping up with the activities. It can take a lot of self-discipline to learn the material and keep up with things without a teacher constantly reminding you. It's actually pretty good practice for vet school, IMO. However, in some cases there are podcast lectures that you can watch. I even took a land-based class once that also had a video component, so that people could turn to the school's cable channel and watch the lecture and complete the requirements without actually having to be at the school.
Good luck! Taking online classes can be really rewarding, and it's really good to be adaptable to different styles of learning/being taught.
