I want to suggest Solid Edge from Siemens. You can use their pipe routing that will automatically create pipe fittings in the intersections, or their magic pipe tool that will allow you to bend pipes and will create weldings on the intersections.
You can get a free trial for Solid Edge from their website, so you can deside before purchase. There is also a free version for students. You need to contact sales to get the paid version.
Do not confuse Solid Edge with SolidWorks, which I will also suggest. The means to do pipe to pipe welding seems to be more involved in SolidWorks.
See the video SolidWorks Tutorial #1: BMX Bicycle Frame from SolidWorks and CAD Tutor, Azeez Salu that demostrate all your requirements.
SolidWorks is a paid product, the purchase method requires to contact sales, even for a demo.