press forward/push on // the lash of public opinion(s)
a. "David encouraged me to keeping pressing forward so that my business would succeed."
b. "The hikers decided to press forward through the night, even though they were dead tired."
→Are the two sentences both correct? What does "press forward" mean? Can I use "push on" instead? Is there any difference between them?
"The lash of public opinion compelled him to resign."
→Is this sentence correct? What does "the lash" mean? Can I pluralize the word "opinion" here? If I do pluralize the word opinion, is there any difference in meaning? Will you pluralize it?