Is it safe and okay to use jpg for printing as well?

Yes, JPEGs are OK for printing but make sure to save them with Maximum quality: 12.

The quality of a JPG will depend on how much it has been compressed, apart from that the difference between a TIF and JPG  is imperceptible IMO. You can also place native Photoshop (PSD) documents in InDesign.
The correct terminology for a raster image displayed on a screen is PPI (Pixels Per Inch), DPI is Dots Per Inch and is used to denote the resolution of a printer such as a laser printer.

The resolution of an image placed in an InDesign document will depend on the dimensions you've selected (the larger the size – dimensions – the lower the resolution). You can check that in the Links panel as the Effective PPI. The normal rule of thumb is 300PPI for books and magazines. For items viewed from a distance – like posters – you can have a much lower resolution than 300PPI.