You really need to acquire several years of basic HPLC training before proceeding so please be sure to work with an experienced chromatographer on your project. It takes many years of industrial training and experience just to acheive a basic level of experience with HPLC and LC-MS takes much longer. Success requires help. Damage to the HPLC and MS systems may result from chemically incompatible additives in your mobile phase (e.g. * HFIP is not compatible with many HPLC vacuum degassers; https://hplctips.blogspot.com/2015/08/an-often-ignored-hplc-lcms.html).
Here are some general comments regarding your other questions.
A, B or A + B: You can add ion-pairing agents or bases such as TEA to both solutions of a binary mix or only add it to the aqueous phase (adding to both solutions may help minimize some of the signal changes as composition changes over time). *Due to solubility issues, it is often best to only add them to the aqueous solution. Please use FRESH, high purity grades with solutions. The additive solutions may degrade quickly after opening so purchase in the smallest sizes. Make up fresh solutions each day. Some additives, such as TEA and TFA, may negatively impact UV response, suppress ionization and/or contaminate the LC-MS source and column used ($$$$). Always label any columns exposed to these additives and never use them for other applications/samples. Their surface chemistry is often changed after use. **Columns are inexpensive consumables.
Additive Amount: Changing the amount of TEA used in a solution is not how to best adjust pH. pH is just one of many parameters which relate to the formation of ions. Please have someone with formal training in LC-MS fundamentals assist you to develop a method that is appropriate and safe for the instrument.
Flushing & Equilibration Steps: (1) First, properly FLUSHING and cleaning an HPLC column, then equilibrating it properly are classic fundamental skills that must be learned early on. Be sure to develop a column wash solution that is STRONGER than your mobile phase for use in washing down the column before each use (after the analysis). (2) Next, using your analysis method as a template, create a separate column equilibration method. An equilibration method must always be run at the SAME flow rate as the analysis method. It should always use the mobile phase initial conditions (for gradient analysis) for composition and be run for as long as it takes to stabilize. The required time must be determined experimentally (don't base it on a generic # of 'column volumes'). Depending on the column type used, the specific mobile phase solutions, the temperature, delay volume of the system and so on, it may take just a few minutes or an hour plus. Such examples as "10" or "20" column volumes are just guesses as no one can answer this question. It will be more than 3 column volumes for sure, but only true scientific experimentation on YOUR instrument will determine how long is 'long enough' for YOUR application and method.
Bong Kyo Seo: As you are new to HPLC and LC-MS, here are some links to free articles which may help you get started in learning a few basics of method development. They include tips on additives, column flushing and equilibration, gradient method design and related topics.
Modern HPLC Method Development Tips (PART I): https://hplctips.blogspot.com/2016/07/modern-hplc-method-development-tips.html
Modern HPLC Method Development Tips (PART II): https://hplctips.blogspot.com/2016/08/modern-hplc-method-development-tips.html