Body Fat % What is normal??

Based on your pictures, I would say neither. The digital caliper is an older device that I used to see when I was right out of school in the mid-1980s. There have always been tools that have attempted to estimate body fat while either a) minimizing the "personal" contact of skinfold measurements and/or b) minimizing the need to find and pay trained professionals to carry out the test.

Skinfold calipers, when used by someone who is both trained AND experienced, are still one of the best methods overall for estimating body fat in average to overfat individuals (they become more inaccurate with increasing obesity). Unfortunately, it doesn't appear that the "trainer" at the Y fits into either category.

Because of body image issues and the dangers of eating disorders, there has always been controversy about what constitutes a "normal" or "healthy" level of body fat for females. The discussions often include as much ideology and politics as they do science.

In the textbooks I used in graduate school 25 years ago, the commonly accepted "ideal" range for women was considered 18% -22% (12%-16% for men). However, others argued that anything up to 30% in women should be considered "normal".

It comes down to how you define your terms (and that is where the ideology and politics come into play). The first criteria should always be health, including morbidity and mortality. In other words, what level is body fat is associated with the lowest health risk? You can usually graph levels of a lifestyle factor (in this case BF%) along with all-cause mortality or associated onset of disease state (hypertension, heart disease, diabetes, etc) and look for a break point at which an increase in BF% is associated with an increase the incidence of disease or all-cause mortality. The "level" part of the graph is considered the "ideal" level and the cutoff point is where bad things start to increase.

Well nothing is that clear cut. Those who, for whatever reason, favor a more strict cutoff, opt for a lower number. Those who are more concerned with the other negative effects of what they considered unreasonable body size expectations for women look at the same data and choose a different endpoint. On any graph of risk factors, health risk increases only mildly at first, at then more steeply as the risk increases (which is why, for most people, the first 10lbs you lose has a much more significant positive effect on health than the last 10lbs).

Other than health, other criteria might be how you are able to function physically and, yes, how you look (by your own standards, not anyone else's).

Because so many people in our society are overweight, there is a tendency to "inflate" the "recommended" standards so that we all feel better about ourselves. Those "recommended" ranges I cited earlier are considered pretty aggressive these days, but they are still valid IMO.

Back to skinfolds. As I said, they can work pretty well for a lot of people, but there are some methodological issues that can affect results. Not everyone is that skilled at measuring the skinfolds accurately. There are some body types (particularly men with a lot of visceral abdominal fat and women who are "apple" shaped) for whom the technique and the equations are a poor match. And some people have skin that doesn't "separate" that well and so it is hard to isolate the skinfold. These are things that are not listed in textbooks and they are not taught in school. You learn them through years of experience and grabbing thousands of folds of skin.

Again, based on your pictures, I would guess you are in the 22%-25% range.

I'm no expert, but I did find the following:

The average for men is 6-15% and women 12-22%.

"Average" being that your hormone levels are good. If you have any untreated health issues affecting hormones, or if you are taking any meds with hormones (ie anti-depressants, birth control, etc), it can affect whether or not you can/will fit into the average body fat ranges.

I've never calculated my body fat % before. Is it something I can do manually at home with a measuring tape or should I buy a device for this?

I wanna know too

The Bod Pod and/or hydrostatic testing are very accurate (about 1% margin for error). I know around here you can get a Bod Pod done for 30 bucks, well worth it. But I agree, a skinfold measurment done by someone with lots of training and experience can also be just as effective, and I also agre DEXA is the most accurate way to have it done (but very expensive).