Electronic – DIY 12 Volt UPS

1. Go with the schottky if you can. In your design, the leakage current will actually charge the battery a bit. This prolongs battery life if the battery can handle this extra current. Example: if you have a 10amp-hour battery with 10 year life, its self discharge current is 114 microamperes; if your schottky has less leakage than that, you can use it.

2. It is sufficient, as long as your Vcc is always > (3.6 + Vdrop) volts

3. Your regulator will only decrease voltage, so putting the battery after regulator and keeping everything the same will not help. The advantage of putting battery after regulator is longer battery life: regulator drops at least 0.1-1.5 volts, so your load will not see full 3.6 volt if battery is before the regulator.

4. Diode is quite good. If you are really concerned about voltage drop, two mosfets and a special controller will be more efficient, but will make design significantly more complicated.

You don't need any switching. Since it is an SLA battery, just run your load from the battery all the time. Let the LM317 keep the battery topped off through D1, or buy a 6V trickle-charger. Adjust the LM317 output until the battery float voltage is at an appropriate level (maybe around 6.5V or 6.6V, but look it up).