Once initiative has been decided, the Round is made up of each creature's turns. Your turn is generally comprised of Actions and Bonus Actions, but a specific turn can include a reaction. You can only take Actions and Bonus Actions on your turn within a round. Your Reaction can be taken on your turn or on someone else's within the round.
On your turn, you are able to Move and take an Action. Examples of actions can be found in the PHB (192-3) and include Attack, Cast a Spell, Dash, Disengage, Dodge, Help, Hide, Search, and Use an Object.
There is one Action you can take that will use your reaction if you choose to use it after your identified triggering event as well: The Ready Action. Should you take this, you have an opportunity to use your Reaction to take an Action based off of a triggering event. Rules for this can be found in the PHB on page 193.
If you have an ability, spell, or some other means where a Bonus Action is available to you, you may use one on your turn.
These are typical in response to a triggering event. Either one that you decide, As with the Ready Action or one that is used as defined by another class ability or spell. An example of this is Counterspell (PHB, 228)
As some reactions can be taken on or outside your specific turn, such as Ready and Counterspell, others can be taken later or earlier in the round, such as Counterspell or Shield - a character is able to use Actions, Bonus Actions, and Reactions during the Initiative Round.
Of course, the standard rules regarding the number of Actions or Reactions still remain and must be followed. While there may be more than one Action available to a player, there is never more than one Bonus Action or Reaction available for a player in a round.
Example 1 - No, Tim would not be able to do this. He has spent his Action casting Fire Bolt. He can't prepare Ready Action because he no longer has an Action to spend.
Example 2 - No, Tim is still limited by his use of his Action casting Fire Bolt. If he had another Action available (e.g. Fighter's Action Surge), he might be able to set up that reaction, but it takes an Action in order to have a Reaction. There are numerous other roadblocks to why this example fails (Readied actions require completion of trigger - so a defensive buff would be 'too late' and that you can only ready a spell with a 1 action cast time.)
My Example of an Action and Reaction on same turn
Tim casts fireball at a group of enemies using his Action. It is now the turn for the enemy Wizard, who follows up with his own Fireball. In response, Tim uses his Reaction to counterspell it.