Is the Eccotemp EL7 enough for a whole house?

Usually not. It is best for one or two hot-water outlets at a time, such as a small apartment, cabin or single bathroom. Whole-house use with several fixtures at once will outrun it.

Does it need venting or a gas line?

No. It is electric and indoor-mounted, so there is no flue or gas supply. It does need a dedicated electrical circuit sized for its draw.

Can I install it myself?

Plumbing is straightforward for a handy owner, but the electrical circuit usually needs a licensed electrician and a permit. Check local code before buying.

How does it compare with a tank water heater?

It saves floor space and never runs out of stored hot water, but its flow limit is lower than a tank feeding several fixtures. A tank is simpler to install and cheaper to wire.

Why does the water cool when I open a second tap?

The unit heats only the water passing through it, so splitting flow across two fixtures lowers temperature at each. Run high-demand fixtures one at a time.