Asking if you can connect any sensor with/without libraries is so broad no one could answer it and the library(ies) needed would depend on the sensor.
The sensors you mention are going to need a level shifter (like this one from Adafruit) or a voltage divider (as discussed in the links below) since they work on 5v and the Pi GPIO can not accept 5v logic. ModMyPi has a good tutorial on the ultrasonic sensor. This question covers the usage of a waterflow sensor.
Both of the links use the RPi.GPIO library which is either easily installed or already on your Pi. If not already installed you can do so with the following command:
sudo apt-get install python-dev python-rpi.gpio
You do not need an arduino. You can connect the sensors to the GPIO pins (with the caution that you will need a voltage divider or level shifter between the sensor and the GPIO pins).
Give your experience level you may want to pick up either Make Sensors or Getting Started with Raspberry Pi. I have read both and they are a great introduction. They will easily payback their price by keeping you from damaging your Pi and include source code that will make your projects easier.
Also, buying parts from China, ebay etc. may seem like a good idea since they are cheaper, but especially for someone just starting out I would suggest spending a little more money and purchase from Adafruit or a similar reseller. This has several advantages:
- They provide support for their products.
- They often have complete tutorials including libraries and sample code. They also regularly update these as required over time.
- They ship fast. depending on where you are in the world, you are likely to receive your parts much faster. It can take a month or more to get parts from China to my home in CT. With that long a wait it is easy to loose interest in a project, or to even have to relearn some of what you know.
In the end the extra cost for the parts is well worth it until you have some experience under your belt.