Can I share the VCC (5V) on my Arduino Pro mini with multiple modules?
Yes, you can do that as long as the total current draw of the modules you attach to VCC doesn't exceed the on-board regulator maximum current output.

The Arduino Pro Mini has a MIC5205 regulator capable of delivering up to 150 mA, which is quite low if you plan to attach many modules to its output. So you should look through your modules datasheets and find out the total current draw, including the Pro Mini board itself, and check that against the 150 mA limit.

According to the HC-SR04 datasheet, each module draws 15 mA. The Arduino Pro Mini itself draws about about 20 mA. The BLE module peak current consumption is 12.5 mA at active RX and 11 mA at active TX, so lets say 25 mA peak current draw for the BLE module.

Everything adds up to a worst case 105 mA peak current draw, within the maximum 150 mA limit. So it should be fine, but I would avoid connecting much more modules to that VCC rail.



ADDED according to your additional question:

If you run out of digital I/O pins, you can use the analog pins as digital pins if needed.

Additional note (thanks go to @jwpat7 for pointing this out in the comments):

However, this is true only of A0–A5 on most Uno and Nano Micro Arduinos, and not true of A6, A7 (except on -PB MCU models like ATmega168PB and ATmega328PB, where A6, A7 can be used as digital pins).