The MIT license is so simple, you should be able to find the answer to your questions by just reading it. It has only one requirement:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
This means that you have no obligation to specify that a program is a derivative work, nor to track the modifications that you made.
For merging several MIT licensed software, you just have to copy the various notices (that is copyright statement + text of the license). If the license texts are exactly the same (the authors did not alter the original MIT license), then it is acceptable to just put the text of the license once, after the various copyright statements. E.g.
Copyright (c) 2017 Your Name
Copyright (c) 2015-2016 Previous Developer's Name
Copyright (c) 2014-2016 Other Project Developer's Name
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE