O2 sensors do not need backpressure to work. as long as it is located within a foot or so of the exhaust manifold and there is a few feet of pipe after the o2 sensor so that oxygen cannot migrate upstream to the o2 sensor it should work fine. Obviously you need to fix all your vacuum leaks - check an replace all hoses as needed as this indeed can cause all sorts of problems.
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84 NB, 3800SC, E-30 Fuel, VS Cam, 3.0 Pulley, 4T65E-HD, HP Tuners, AEM Wideband, Regal GS Gauges, S-10 Brake Booster. 12.53 at 106.5 1/4 mile