It’s very much available like reach kalka via train or bus and go on toy train to shimla that is the best mode.
Second is direct local buses from chandigarh to shimla
Hire a cab to shimla
The first option is the best..book tickets in advance and reach there and travel around on your own..for distant places you’ll get plenty of cabs there also n cheap also
Yes it is possible but it will be inconvenient for you and a lot of trouble for you. Instead you can opt for a package. I have attached with this comment few packages for you, you can click on them to find more details about them. If you want to talk to someone about the packages simply fill in your details in the form and you will receive a call.