Do inflows influence bond prices and/or yields

As in any market, purchases will bias the price process to be higher than without buying. Much of market microstructure research shows that for theoretical reasons and confirms it with empirical work.

Fixed income ranges from much more liquid than most equities (US Treasuries) to far less liquid than equities (municipal bonds, very small corporate bonds, emerging market debt). A thorough overview is Bessembinder, Spatt, and Venkataraman (2020); you might also find this 2016 BIS CGFS paper informative. Finally, Ottonello (2019) shows that inflows to bond funds tend to push prices higher (and thus yields lower).