No there is nothing like this that there will be no placement.
You can get placement definitely.
There are many options.
Like btech
Bsc
Defence.
Pharmaceutical
Aerospace
Merchant Navy.
Army Navy
Air force from NDA.
etc.
According to your choice you can go with anyone
Hope you will achieve success.
Good luck.

You go airforce after 12th you are now eligible for NDA exam 1 of the best career.

It's okay if you dropped for one year. Many candidates take a drop for a year due to entrance exams and other certain reasons. Now make sure you don't waste your time from now on. Admissions for next year would began in next 4-5 months. 

Coming to best course. Well all of them are best. You just have to figure it out which one is best for you. Where your interest lies? If you want to learn pure sciences and go for research then you can go for BSc then MSc and then PHD. If you want to learn the applications of vast discoveries of Science then you can go for Engineering.

This is very basic. There are many branches in both BSc and and engineering . And placements all depends upon skills you have. Almost in all universities and colleges a candidate who has taken a drop for a year are accepted. Some of them only ask reason for taking drop reasons. 

Find out where your interest lies. For engineering there are various entrance exams held for taking admission in colleges both government and private. So if you want to do engineering then you have to prepare for them. 

If you still have any queries feel free to ask in the comment section down below .