Those are very good questions. The first one is hard to answer, because the global bird population is changing all the time. Also, many birds live in places that are hard to reach, where people don't often get a chance to observe and count them. But there have been some reasonable estimates.
About 10 years ago, two scientists decided to estimate the total number of birds on the planet. The number they came up with was 200 to 400 billion individual birds. Compared to 5 billion people, this amounts to about 40 to 60 birds per person.
Your second question, unfortunately, is much easier to answer. The world's bird population is definitely decreasing.
Since the 1500s, birds have been declining both in terms of species numbers (by about 500 species) and numbers of individuals (by about 20-25%). This decline is due to human activities, such as the cutting down of forests, contamination, invasive species, and human-induced climate change.
By the year 2100, up to 14% of all bird species may become extinct. And 7-25% (28-56% on oceanic islands) may become "functionally extinct." It means that the number of individuals within these species will become so low that the species will no longer play an important role in their ecosystem.
Birds are a vital part of ecosystems and they perform important tasks. For example, birds pollinate and disperse the seeds of many plants, including many crops important to humans. They are also helpful in controlling crop pests. And scavenger birds like vultures help with the decomposition of organic material.
All of these benefits to humans and other organisms will likely decline along with bird numbers and species. Because birds can have an important role in controlling other organisms, their decline may even encourage the spread of disease.
The good news is that conservation actions worldwide are slowing the path of extinction of many species. Many concerned people are also becoming involved in local conservation initiatives. They help count, track, and protect birds in their communities. Their efforts can make a significant difference!