Can I statically link Apache2/ISC/MIT/BSD licensed libraries to my project that is under GPL (v3 because I've learned that v2 isn't compatible with Apache2) and create an executable binary?
BSD license requires you to add some messages to your binaries:
Redistribution and use in source and binary forms are permitted provided that the above copyright notice and this paragraph are duplicated in all such forms [...]
MIT license requires you to add some messages to your binaries:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
Apache License version 2 requires you to add some messages to your binaries:
Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions:
a. You must give any other recipients of the Work or Derivative Works a copy of this License; and
b. [...]; and
c. [...]; and
d. If the Work includes a "NOTICE" text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. The contents of the NOTICE file are for informational purposes only and do not modify the License. You may add Your own attribution notices within Derivative Works that You distribute, alongside or as an addendum to the NOTICE text from the Work, provided that such additional attribution notices cannot be construed as modifying the License.
You may add Your own copyright statement to Your modifications and may provide additional or different license terms and conditions for use, reproduction, or distribution of Your modifications, or for any such Derivative Works as a whole, provided Your use, reproduction, and distribution of the Work otherwise complies with the conditions stated in this License.