Most of the metrics you would like to see are accessible through the respective applications statistics, which is much more effective than log analysis. And there are several free projects aimed to collect such metrics, build graphs, check margins, send warnings, etc. All of them are designed to be easily extensible, so that a lot of plugins for collecting metrics exist and you can write your own. The names of the main projects I remember of are Munin, Cacti and Graphite, but in fact there are more.
Munin is one of the oldest and has a lot of plugins even in the standard package. From your list:
- server load Munin has plugins to show load average (LA), iostat, vmstat
- Nginx Munin has "nginx_request" (req/sec) and "nginx_status" (number of connections in a specific status, i.e. active, reading, writing)
- response time As far as I know, there is no such plugin. See this question for more information
- MongoDB MongoDB team provides several Munin plugins at GitHub