Can I download Grabcad parts and use them in an assembly at work without any trouble ?
what kind of trouble are you worrying about? Just don't take credit for other peoples work, and be clear about your sources for models you didn't create yourself.
Keep in mind, product verification (dimensions, material, etc.) still lies on you, there is no guarantee the models on here are perfectly accurate, so use them at your own risk.
make your own
It depends on what kind of model. If is it some standard tools that are missing in the toolbox, then upto a point it is alright to use them, given that, you have their permission or give them credit.
Other option is reverse engineering i,e. If you can download the files then you can easily recreate them. But again, if it a mechanism or some model with lot of hard put it, it would amount to theft of intellectual propoerty.
The best way out, as always, sit and work it out for yourself. you have nothing to worry about and will have great satisfaction. :)
Yes you can. However, be sure to site your source/engineer and give credit where it is due. Not all models you download or use will be 100% accurate so make sure you take that into account also.
Thank you for your comments, i will give credit to the designer.