
1) Felt/Feeling
Although there are certain situations that call for people to feel something, in many cases you can eliminate the word itself.
Compare ‘She felt a deep love for him’ with ‘She loved him deeply’.
Both these sentences say the same thing, but the second option has far more impact.
2) Thought/Thinking
The same holds true for things a character thinks.
Compare ‘She certainly thought it was unusual’ with ‘It was certainly unusual’.
We’re already in the character’s POV; therefore, we know that she’s the one thinking ‘it’s unusual’ without needing to be told so in the prose.
3) Started to/Began to
In some cases it does make sense to use one of these phrases. For example, they are necessary if you plan to interrupt the action the character is performing before they have completed it. However, most of the time they aren’t needed.
Compare ‘She started to run down the corridor’ with ‘She ran down the corridor’.
Both are true, yet the second has more immediacy and suggests a greater urgency to the action. I would only use the former if you plan to continue the scene with something along the lines of 'but after a few steps, she tripped'.