Is there a total number of awards that a battalion can give for a field exercise ?

Indeed there is no authority to limit quantities of awards. Each submitted award is to be considered on it's own merit by the approving authority level for the award. such as a BN commander (LTC typically) is the approving authority for an AAM. A platoon leader or company commander can recommend disapproval but the award still goes to the approving authority (the BN CDR). The BN CMDR can recommend only approving a certain amount for some reason I can not myself justify why and those below him/her may be resistant to press that general guidance but I think it is an injustice to those individuals who are perform acts and duties that merit the award by powers far greater and more experienced then those low level commanders. I wish you luck and if you choose to take the path of the "Hard Right" versus the easy, press to make all award go to the approving authority as they should and make them downgrade or reconsider the assumption that only a few soldiers each training exercise could possibly achieve outstanding performance. I would also empower yourself with trying to get feedback from the S1 NCO & Officer on what a good award write up looks like before submitting it. Also, try and attain copies of awards that were approved from the approving authority to see what he/she wants to see and expects merits the award being recommended. Also you can find the awards written up for the next level high award (my example above would say find what is need for an ARCOM) and was approved for the ARCOM or at least accepted as a downgrade and approved for an AAM. Learn to write awards the way this individual likes to see them to improve success. The regulations does say spelling and grammar are not a reason for rejecting a submission but I can say, I have never met a commander that would move it forwarded without good grammar. Use your S1 folks, they are used to seeing quality evaluations and awards and can help a lot.

AR 600–8–22 dated 5 March 2019
Chapter 3
Paragraph 3-1 (note item f)

3–1. Intent
a. U.S. Army military decorations are awarded in recognition of qualifying acts of valor, non-combat heroism, or meritorious service or achievement.
b. Servicemembers who perform valorous actions or demonstrate non-combat heroism will be accorded appropriate recognition based solely on the merits of their actions. Such awards should recognize the specific act(s) of valor or noncombat heroism. Awards for valor and heroism will be limited to a specific (usually brief) time frame in which the act(s)
occurred.
c. Individual awards for service or achievement are intended to recognize significant contributions to the mission accomplishment, readiness, effectiveness, morale or esprit de corps of a unit or organization. Recommendations for awards must be justified by specific achievements, contributions or other notable impacts. The award should reflect both the individual's level of responsibility and manner of performance. Exceptional command or leadership at any level, in and of itself, may be considered meritorious achievement or service. Ultimately, individual awards for service or achievement will be performance based.
d. The decision to award an individual a decoration and the decision as to which award is appropriate are both command decisions. The Army entrusts commanders to exercise awards approval authority based on the merits of each individual recommendation.
e. Award approval authorities may make award decisions without referral to a local awards board. Awards boards are optional and are at the discretion of the approval authority. Use of such boards should not add additional processing time that violates processing timeline guidance in paragraph 3–21.
f. Rank/Grade will not be a factor in determining the type or level of recognition, nor will any quotas be established limiting the number of awards that may be recommended or approved.
g. No individual is automatically entitled to an award upon departure from an assignment.
h. No award is automatic and preconditions for an award may not be established. Examples of inappropriate preconditions include:
(1) Attainment of specific goals that automatically result in an individual award (300 Army physical fitness test = AAM or Top Gun = ARCOM).
(2) Awards used as prizes in contests.
(3) Policies prescribing specific awards for specific ranks or specific periods of service (3 years = ARCOM).
(4) Policies limiting eligibility for awards beyond the Army established minimum standards.
50 AR 600–8–22 • 5 March 2019
i. Certificates of achievement and letters of commendation or appreciation are appropriate means to recognize departing personnel, periods of faithful service, acts or achievements which do not meet the standards required for decorations (see para 10–7).
j. Unless otherwise stated, an individual who is eligible for a DOD Joint award will not be recommended for an award through their parent Service unless an appropriate DOD Joint award does not exist.

AR 600–8–22 dated 5 March 2019
Chapter 3
Paragraph 3-1.F
Rank/Grade will not be a factor in determining the type or level of recognition, nor will any quotas be established limiting the number of awards that may be recommended or approved.