A. First, HOSTS and LMHOSTS files apply only to TCP/IP, not to IPX and SPX. NWLink uses NetBIOS exclusively as the default namespace to resolve network names—as evidenced by the NetBIOS-related error message you received.
If the systems all reside on the same segment, you should have no problems. NetBIOS name resolution should occur through broadcast, as long as you've properly configured Pervasive.SQL 2000 on the client and server to work with IPX-based connections. (This tricky configuration can be a potential roadblock. I've wrestled with Pervasive.SQL clients—and their Btrieve predecessors—many times in the past.)
If you're using IPX and multiple segments are involved, the intervening routers might not be configured to pass NetBIOS traffic (e.g., through bridging or Cisco's "smart" IPX-based NetBIOS proxy-ing), which enables machines on various segments to find one another. Regarding your TCP/IP solution, if you believe that WinGate is interfering, you might want to contact Deerfield.com to see whether the company provides a facility to bypass the use of the WinGate proxy for specific connections.