Teaching subjects as an instructor which I scored average grades in As a final year PhD student, I have been asked to teach a short introductory course on solid mechanics for undergrad students. Now, my PhD research has been applied mechanics where I developed tools and carried out fundamental research on a manufacturing process. But, it was quite away from what we get taught in our undergrad and grad courses. 

I had taken solid mechanics course during my undergrad time, but I remember not scoring well in my tests and assignments. Infact, I had got a B+ grade in the subject. I am confident about my knowledge on the important concepts, derivations and theories, but I am poor in solving problems at the back of the chapters.

I am wondering if anyone can give me some advice on how to prepare assignments and questions for the course? I will be taking 6 lectures, 2 out of which will involve giving a hands-on training on a software that I use for my PhD research.

I am worried about the first 4 lectures and developing assignment questions for the class. I have 3 weeks to prepare.
First, you are doing well to focus on exercises. Student activities are the most important part of any course preparation. In general, it is much more important what the students do in a course (exercises) than what the instructor does (lectures). 

If you can recommend a textbook to the students it will have exercises from which you can choose. Or, you can tailor some of them specifically to the material you will be teaching if the book is a bit too general. 

Alternatively you can adapt exercises from a variety of textbooks. An interesting way to do this is to give exercises from various books but cite them explicitly so that the students have an opportunity to go to those books (in the library, perhaps) and read some context to help them. 

Finally, let me note that for your own learning, teaching a course in a subject is likely to deepen your own understanding of it. This is partly due to the reinforcement you get from preparing lectures, but also from responding to student questions and having to actually find ways to explain things in a way they can grasp. 

As for the software, some exercises that depend on its use to solve some simple problems is good, but I suspect you know that already. 

A trick for connecting to your students is to admit that the material is hard and that you also found it so as a student. This will put them on notice that they need to apply themselves, but will also make you more human and accessible in their eyes. This may be desirable or not. It is considered a good thing in the US, but perhaps not universally.