Can I connect my phone line to my ADSL modem without the ADSL splitter? ?

Yes, however, if your phone lines are not adequate, you need to call the phone company and have them set your line up for DSL

if you have bought ADSL you should have a splitter

but you can go without splitter (with network though), as long as you're not planning on using your phone

The buzzing sound may be due to lose wiring. Check it out beacause when two wire are joined it cause an increase in load to the system.