Computationally and logically, it's prudent to minimise the number of inputs to a system so the system performance is still maximised. Adding inputs which are not used (or ignored) is pointless and should be avoided. Adding too much "information" (or noise) can lead to "analysis paralysis"; if you only need x-indicator in agreement with y-filter to trigger a trading response, there is no point in computing or plotting anything else.

If you omit information necessary to maintain the system performance at its optimum then you'll be reducing the system performance and may end up destroying it; it's a fine balance.

An interesting question, a question to which there is no definitive answer.

There is very little point in computing highly correlated indicators, as all this does is give the trader a warm, fuzzy feeling without giving any new information on which to base the trade; unless of course, your system is based on exploiting the times when the correlation suddenly changes (or diverges), or each component is required to work dependently with its correlated partner. (Both and none at the same time!)

You need to fully understanding the construction, capabilities and limitations of every indicator you want to employ e.g. take EMAs. You open a chart and plot the EMA10, EMA20 and EMA50. The EMAs are all neatly stacked; the price is above the EMA10 which is above the EMA20 which is above the EMA50 and they have been neatly stacked like this for quite some time. What does this indicate to you? For some (investors or traders, it doesn't matter) they might see the confirmation of an uptrend and will enter the trade right away. Some traders might see this as a missed opportunity as they believe they should have got in when the prices first became ordered, so are going to ignore this chart for now and move on. Some will start watching the chart, waiting for the first sign of weakness. How they see the data is irrelevant; how you see the situation is the only thing which is important?

There is a school of thought to which many traders subscribe: individual trade signals are generated based on individual charts, but filters should be based on broader market data. You might utilise some RSI or MFI indicators on a stock chart as triggers, but you might ignore (or filter) generated long trading signals if three EMAs aren't in the correct orientation on the relevant index chart. But, this might not suit your trading style?

Lots of people have spent a LOT of time employing massive neural networks, genetic algorithms, self-organising maps etc to try and decide the best inputs to a system which delivers the best outputs (I should know, I'm still toying with several different ideas now). No-one has discovered the Grail, no-one has a panacea of inputs which works for every trader in every market all of the time, nor will they. What they might discover is one fine 'edge' that gives them an small advantage for a short time, before they will have to retrain and relearn.

You have to figure out what works for you, then decide on how and when you are going to measure the performance or success of your system and what conditions will have to be met for you to drop/reconsider your system.

A very simple example:

Buy if C(stock)>EMA20(stock) and C(Index)>EMA200(Index)

Such a "system" would prevent you from entering long trades when the market (as described by the index) was not in an up-trend (defined by the index price vs. its EMA200).

Whether you choose the whole-of-market index, or a sub-sector index, or currency exchange rate, interest rate, commodity price etc is up to you.

I cannot define "better" for you; only you can do that.

Instead of supposing, postulating and hypothesising, why not use some of the tools at your disposal, such as the Enhanced System Tester to test some of your theories to see if you can better define for yourself "what makes sense"?

“If I had an hour to solve a [question], I'd spend 55 minutes thinking about the [question] and 5 minutes thinking about solutions.”

- Albert Einstein