1.pluto is a slow planet. do some inner planet transits show extreme tense periods too??
They can, especially if what they're doing is making a hard aspect--opposition or square--to the sun, moon, or a personal planet. But the faster the planet moves, the faster the tension passes. If there's a slow moving planet like Pluto aspecting something in your chart, and then an inner planet gets involved in that aspect, it intensifies while the inner planet is there. But it's only a matter of days.
When a planet is on a sensitive chart point, its energy is strongly felt in the native's life. If it's an inner planet, it passes quickly, it might be just a momentary thing. If it's a slow moving planet, it stays on that point long enough to make a profound change in the person's life. In Pluto's case, it's an energy of transformation, but it can be felt in a destructive way.
Right now, Pluto is within a couple degrees of your mom's IC. That puts its power in the home/family/land/deep self identity arena for her.
You said your father is sick? If your mother is dealing with a seriously ill husband, that's a transformation in her home life right there. Becoming your spouse's caregiver is a Plutonian kind of change.
That says nothing about whether he'll die of this illness or not. Even if he survives, it's still a transformation. It's still Plutonian.
IC opposes MC, so a transit to the IC typically means a shift in career or public image as well. Does your mother work outside the home? Or did she in the past? If that's changing around now, that would be reflected by Pluto. Or maybe it's her public image. With MC in Cancer, it seems likely that she was known in the community as a mother, or that if she has a career, it's something associated with family/mothering. If all of her children are grown now, the public mother identity would be changing.
2.once its identified this period is extremely tense-what to do then???are there any coping mechanisms??
Depends on the real world reasons why it's tense. Astrology only reflects what's going on in our lives. If your father is sick, the support for your mother would be whatever normally would support people with sick spouses.
3.you can tell me any characteristics she needs to develop, if its possible to find out from the chart.
That would require your mother herself being part of the conversation. The chart doesn't tell us what characteristics she's already developed, just what the potential is. By her age, much of the potential would be developed already. At that time in life, it's more about working with what you already have, than about who and what you will become.